Methodical Approaches to Describe and Evaluate Uncertainty in the Transmission Behavior of a Sensory Rod

2015 ◽  
Vol 807 ◽  
pp. 205-217
Author(s):  
Christiane Marianne Melzer ◽  
Martin Krech ◽  
Lisa Kristl ◽  
Tillmann Freund ◽  
Anja Kuttich ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Electrical Properties ◽  
Development Phase ◽  
Electrical Transmission ◽  
Young’S Moduli ◽  
Mechanical And Electrical Properties ◽  
Load Carrying ◽  
Piezoelectric Charge

Load carrying mechanical structures like trusses face uncertainty in loading along with uncertainty in their strength due to uncertainty in the development, production and usage. The uncertainty in production of function integrated rods is investigated, which allows monitoring of load and condition variations that are present in the product in every phase of its lifetime. Due to fluctuations of the semi-finished parts, uncertainty in governing geometrical, mechanical and electrical properties such as Young's moduli, lengths and piezoelectric charge constants has to be evaluated. The authors compare the different direct methodical approaches Monte-Carlo simulation, fuzzy and interval arithmetic to describe and to evaluate this uncertainty in the development phase of a simplified, linear mathematical model of a sensory rod in a consistent way. The criterion to compare the methodical approaches for uncertainty analysis is the uncertain mechanical-electrical transmission behavior of the sensory rod, which defines the sensitivity of the sensory compound.

Analysis on Motion Precision Reliability of Hydraulic Support

2011 ◽  
Vol 48-49 ◽  
pp. 224-227
Author(s):  
Dong Chen Qin ◽  
Qiang Zhu ◽  
Hong Xia Wu ◽  
Zhe Feng Guo
Keyword(s):  
Mathematical Model ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Theoretical Calculation ◽  
Calculation Method ◽  
Effective Length ◽  
Future Research ◽  
Hydraulic Support ◽  
Continuous Contact ◽  
Continuous Contact Model

In order to research the motion precision reliability of hydraulic support when the influence of the bar length error and gap error is considered, the motion trace mathematical model for the top beam of hydraulic support is established, with the calculation method of motion precision reliability and the effective length of bar based on continuous contact model. Taking some type of hydraulic support as an example, its motion precision reliability is calculated and analyzed. The Monte Carlo simulation is also used to verify the model, and the T-R curve of the gap error and the reliability is plotted. The results from simulation accord with those from the theoretical calculation, which verifies the model established and can provide some valuable reference for the related future research.

A Mathematical Model for Tire/Wheel Assembly Balance

1993 ◽  
Vol 21 (4) ◽  
pp. 220-231
Author(s):  
E. J. Ni
Keyword(s):  
Mathematical Model ◽  
Monte Carlo Simulation ◽  
Finite Element ◽  
Monte Carlo ◽  
Monte Carlo Model ◽  
Element Model ◽  
Equation Of Motion ◽  
Rigid Body Dynamics ◽  
Production Distribution ◽  
Body Dynamics

Abstract A mathematical model is developed to calculate the weight required on a tire/wheel assembly to balance wheel nonuniformity effects such as the lateral runout. A finite element model of a tire mounted on a rigid wheel is used to simulate the free spinning about a skewed axis. The result showed that Euler's equation of motion in rigid body dynamics can be used to calculate the imbalance caused by wheel lateral runout. This equation is then used in a Monte Carlo model to simulate a production distribution. The model can be used to define tire and wheel specification limits, and to predict the number of assemblies that will have unacceptable imbalances. The verification of the model and results of the Monte Carlo simulation are presented.

Cellular Automaton Approach on Micro Solidification Process of Two Phase Alloy in Horizontal Casting

2000 ◽  
Author(s):  
Toshio Tsuta ◽  
Takeshi Iwamoto
Keyword(s):  
Mathematical Model ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Liquid Metal ◽  
Continuous Casting ◽  
Cellular Automaton ◽  
Solidification Process ◽  
Two Phase ◽  
Grain Growth Kinetics ◽  
Micro Morphology

Abstract A mathematical model of micro morphology generation in solidification process has been developed using cellular automaton approach, and heterogeneous nucleations from the wall and the grain growth kinetics are simulated by using the Monte-Carlo simulation. In the next place, the change in the micro morphology from the dendritic to the equiaxial, has been analyzed in the same way, under the condition that the liquid metal in the vessel is excited from magnetic stirrer. The results are compared with those obtained by the experiments on horizontal, continuous casting and the applicability of the method has been verified.

Fatigue Reliability Assessment of Fillet Welded Cruciform Joints Based on the Fatigue Notch Factor and Local Strain Approach

2018 ◽  
Author(s):  
Yan Dong ◽  
Yordan Garbatov ◽  
C. Guedes Soares
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Local Strain ◽  
Simulation Method ◽  
Monte Carlo Simulation Method ◽  
Fatigue Reliability ◽  
Cruciform Joints ◽  
Load Carrying ◽  
Fatigue Notch Factor ◽  
Weld Root

The objective of this work is to analyze the fatigue reliability of fillet welded cruciform joints considering the uncertainty of the load and capacity. The weld shape is defined by multivariate normally distributed variables, which represent the position variations of the shape control points on the fillet welds. Finite element analyses are performed to calculate the fatigue notch factors of the weld root and toe, where the fatigue crack is usually initiated. Various weld shapes associated with various correlation conditions and weld quality levels are generated and the corresponding probability distributions of the fatigue notch factors are obtained by using the Monte Carlo simulation method. Sensitivity analyses are carried out to identify which location is more important for the fatigue notch factors. Within the context of the local strain approach, a critical fatigue notch factor that can exactly trigger fatigue failure is proposed. Its statistical descriptors are determined by using the Monte Carlo simulation method, in which the nominal stress range, material properties and fatigue damage at failure are treated as random variables. The limit state functions of the weld root and toe are formulated based on the actual and critical fatigue notch factors. The first order reliability method is applied to evaluate the fatigue reliability. The cruciform joint, composed by two fatigue-prone locations, is evaluated as a series system of components. Two different loading conditions, which make the cruciform joints load-carrying and non-load-carrying respectively, are considered.

Simulation-Based Parametric Reliability Modeling Using Covariate Theory

2003 ◽  
Author(s):  
Jon M. Wallace ◽  
Dimitri N. Mavris
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Probability Distribution ◽  
Product Development ◽  
Failure Probability ◽  
Proportional Hazards ◽  
Development Phase ◽  
Simulation Data ◽  
Reliability Modeling ◽  
Parametric Reliability

Reliability analysis methods used for preliminary safety assessments of complex systems typically assume a predetermined and invariant set of input variable statistical properties. However, during the product development phase of the system and especially during in service operation, the characteristics of the random variables can themselves be subject to variation. Thus, the resulting failure probability distribution can vary greatly from early predictions. The objective of this paper is to explore a technique used to create a general parametric failure probability distribution as a function of key variables. This technique is constructed around covariate theory which is the basis of the familiar Accelerated Life Testing and Proportional Hazards Modeling approaches. Where these approaches have traditionally been used with physical experiments, they are applied within this study to Monte Carlo simulation data generated using an available component modeling and simulation environment of a gas turbine airfoil limited by a single failure mode. Necessary modifications to the traditional from of the covariate approach are identified for application to controlled Monte Carlo simulation data. Implications to potential safety improvements early on in the product development phase are discussed.

scholarly journals THE SYSTEM FOR SIMULATING INTERBANK SETTLEMENTS

2007 ◽  
Vol 13 (4) ◽  
pp. 323-332 ◽  
Author(s):  
Donatas Bakšys ◽  
Leonidas Sakalauskas
Keyword(s):  
Mathematical Model ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Settlement System ◽  
Active System ◽  
Settlement Systems

The aim of this paper is a study of the system for simulating interbank settlements. Interbank payment and settlement systems establish conditions for the circulation of financial funds on the market and guarantee the distribution of assets. Practical experiments in an active system are very risky. They demand to simulate their operation through a system by creating its mathematical model. By perfecting the processing of settlements and/or developing algorithms for solving the gridlocks or by applying the tools of refinancing and using reserves of requirements, one can change the efficiency of settlement systems. The results of the study by Monte‐Carlo simulation are given, based on data of the payment and settlement system of the Bank of Lithuania.

scholarly journals Generalized mathematical model of cancer heterogeneity

2020 ◽  
Author(s):  
Motohiko Naito
Keyword(s):  
Mathematical Modeling ◽  
Differential Equation ◽  
Mathematical Model ◽  
Stochastic Process ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Stochastic Differential Equation ◽  
Cancer Growth ◽  
Cancer Heterogeneity ◽  
Growth Properties

AbstractThe number of reports on mathematical modeling related to oncology is increasing with advances in oncology. Even though the field of oncology has developed significantly over the years, oncology-related experiments remain limited in their ability to examine cancer. To overcome this limitation, in this study, a stochastic process was incorporated into conventional cancer growth properties to obtain a generalized mathematical model of cancer growth. Further, an expression for the violation of symmetry by cancer clones that leads to cancer heterogeneity was derived by solving a stochastic differential equation. Monte Carlo simulations of the solution to the derived equation validate the theories formulated in this study. These findings are expected to provide a deeper understanding of the mechanisms of cancer growth, with Monte Carlo simulation having the potential of being a useful tool for oncologists.

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