Circular Arc Gear Reliability Study Based on Modified FOSM Method

2013 ◽  
Vol 760-762 ◽  
pp. 2216-2219
Author(s):  
Zhong Li ◽  
Bo Yu Cheng
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Limit State ◽  
Point Method ◽  
Reliability Study ◽  
Circular Arc ◽  
Gear Case ◽  
Improve Reliability ◽  
State Functions

As different limit state functions are used to analyze reliability, there is a great distinctness among the calculated results. In this paper an improved LOSM method is proposed, namely, checking point method. The circular arc gear case is employed to demonstrate this method. In contrast to the results of Monte Carlo simulation, this method can greatly improve reliability calculations precision.

Project Scheduling Problem with Stochastic Resource-Dependent Activity Duration

2013 ◽  
Vol 483 ◽  
pp. 607-610 ◽  
Author(s):  
Chun Jie Zhong ◽  
Ying Yu ◽  
Yun Lang Jia
Keyword(s):  
Genetic Algorithm ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Project Scheduling ◽  
Point Method ◽  
Scheduling Problem ◽  
Resource Constrained ◽  
Activity Duration ◽  
Dependent Activity ◽  
Project Scheduling Problem

A resource-constrained project scheduling problem with stochastic resource-dependent activity durations is presented in this paper,and the two-point method is employed to simulate the uncertain property.Furthermore a genetic algorithm combined with this method is provided to solve the problem. Compared with the results from the genetic with Monte Carlo simulation, the proposed method is verified to be effective and more efficient.

scholarly journals Non-deterministic Approach for Reliability Evaluation of Steel Portal Frame

2019 ◽  
Vol 5 (8) ◽  
pp. 1684-1697
Author(s):  
Hawraa Qasim Jebur ◽  
Salah Rohaima Al-Zaidee
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Structural Reliability ◽  
Limit State ◽  
Computational Cost ◽  
Probability Of Failure ◽  
Ultimate Limit State ◽  
Axial Forces ◽  
Portal Frame ◽  
Ultimate Limit

In recent years, more researches on structural reliability theory and methods have been carried out. In this study, a portal steel frame is considered. The reliability analysis for the frame is represented by the probability of failure, P_f, and the reliability index, β, that can be predicted based on the failure of the girders and columns. The probability of failure can be estimated dependent on the probability density function of two random variables, namely Capacity R, and Demand Q. The Monte Carlo simulation approach has been employed to consider the uncertainty the parameters of R, and Q. Matlab functions have been adopted to generate pseudo-random number for considered parameters. Although the Monte Carlo method is active and is widely used in reliability research, it has a disadvantage which represented by the requirement of large sample sizes to estimate the small probabilities of failure. This is leading to computational cost and time. Therefore, an Approximated Monte Carlo simulation method has been adopted for this issue. In this study, four performances have been considered include the serviceability deflection limit state, ultimate limit state for girder, ultimate limit state for the columns, and elastic stability. As the portal frame is a statically indeterminate structure, therefore bending moments, and axial forces cannot be determined based on static alone. A finite element parametric model has been prepared using Abaqus to deal with this aspect. The statistical analysis for the results samples show that all response data have lognormal distribution except of elastic critical buckling load which has a normal distribution.

A polynomial chaos meta‐model for non‐linear stochastic magnet variations

2013 ◽  
Vol 32 (4) ◽  
pp. 1211-1218 ◽  
Author(s):  
Peter Offermann ◽  
Kay Hameyer
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Flux Density ◽  
Polynomial Chaos ◽  
Epistemic Uncertainty ◽  
Limit State ◽  
Element Model ◽  
State Function ◽  
Content Type ◽  
Meta Model

PurposeDue to the production process, arc segment magnets with radial magnetization for surface‐mounted permanent‐magnet synchronous machines (PMSM) can exhibit a deviation from the intended ideal, radial directed magnetization. In such cases, the resulting air gap field may show spatial variations in angle and absolute value of the flux‐density. For this purpose, this paper aims to create and evaluate a stochastic magnet model.Design/methodology/approachIn this paper, a polynomial chaos meta‐model approach, extracted from a finite element model, is compared to a direct sampling approach. Both approaches are evaluated using Monte‐Carlo simulation for the calculation of the flux‐density above one sole magnet surface.FindingsThe used approach allows representing the flux‐density's variations in terms of the magnet's stochastic input variations, which is not possible with pure Monte‐Carlo simulation. Furthermore, the resulting polynomial‐chaos meta‐model can be used to accelerate the calculation of error probabilities for a given limit state function by a factor of ten.Research limitations/implicationsDue to epistemic uncertainty magnet variations are assumed to be purely Gaussian distributed.Originality/valueThe comparison of both approaches verifies the assumption that the polynomial chaos meta‐model of the magnets will be applicable for a complete machine simulation.

Mechanical Component’s Dimension Design With Required Reliability by the Monte Carlo Method

2020 ◽  
Author(s):  
Xiaobin Le
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Failure Mode ◽  
Failure Modes ◽  
Limit State ◽  
Design Parameters ◽  
Mechanical Component ◽  
Component Design ◽  
The Monte Carlo Method ◽  
State Functions

Abstract Since the main design parameters in a mechanical component design have some uncertainties and should be treated as random variables, the reliability of a component is a better measurement of the safe status of a component. A component will not be reliable unless it is designed with specified reliability. Therefore, the mechanical component design should be a dimension design with the required reliability. The fundamental concept of the Monte Carlo method is to plug-in randomly generated numerical values into the governing equation of a design problem to get a trial result. The Monte Carlo method has become so powerful numerical simulation approach in almost every field such as optimization, numerical integration, and reliability calculation. But for reliability engineering, most of the literature shows how to use the Monte Carlo method to calculate the reliability of a component. This paper will propose the modified Monte Carlo method to determine a component dimension with required reliability. This paper first discusses and establishes typical limit state functions of a component under static loads. These limit state functions cover two failure modes including the failure mode due to strength and the failure mode due to excessive deformation. Then, the procedure and the flowchart of the modified Monte Carlo method will be explained in detail. The provided procedure and the flowchart are easy to be followed for compiling a MATLAB program to conduct a dimension design with required reliability. Two examples will show how to implement the proposed new method for conducting a dimension design with required reliability.

Comparison of Monte Carlo Simulation and Response Surface Method by Using ANSYS PDS

2014 ◽  
Vol 578-579 ◽  
pp. 1449-1453
Author(s):  
Chun Xue Song ◽  
Yi Zhang ◽  
Ying Yi Cao
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Probabilistic Analysis ◽  
Limit State ◽  
Design System ◽  
State Function ◽  
Surface Method

Monte Carlo Simulation and Response Surface Method are two very powerful reliability analysis methods. Normally, in the reliability analysis of complex structures, the limit state function often can not be expressed in a closed-form. Usually, the codes for probabilistic analysis need to be combined with finite element models. ANSYS Probabilistic Design System (PDS) has provided a package to conduct probabilistic analysis automatically. This paper is going to compare the performance of these methods through an easy engineering problem in ANSYS. The results are going to be derived to show the feature of applying the corresponding reliability methods.

Local Monte Carlo Simulation for the Reliability Sensitivity Analysis

2011 ◽  
Vol 291-294 ◽  
pp. 2183-2188 ◽  
Author(s):  
Da Wei Li ◽  
Zhen Zhou Lu ◽  
Zhang Chun Tang
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Numerical Technique ◽  
Limit State ◽  
Computational Cost ◽  
Simulation Method ◽  
State Function ◽  
Local Domain ◽  
Monte Carlo Simulation Method ◽  
Reliability Sensitivity

An efficient numerical technique, namely the Local Monte Carlo Simulation method, is presented to assess the reliability sensitivity in this paper. Firstly some samples are obtained by the random sampling, then the local domain with a constant probability content corresponding to each sample point can be defined, finally the conditional reliability and reliability sensitivity corresponding to every local region can be calculated by using linear approximation of the limit state function. The reliability and reliability sensitivity can be estimated by the expectation of all the conditional reliability and reliability sensitivity. Three examples testify the applicability, validity and accuracy of the proposed method. The results computed by the Local Monte Carlo Simulation method and the Monte Carlo method are compared, which demonstrates that, without losing precision, the computational cost by the former method is much less than the later.

scholarly journals Design of Foundations Against Differential Settlement

2021 ◽  
Author(s):  
Farzaneh Naghibi ◽  
Gordon A. Fenton
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Limit State ◽  
Differential Settlement ◽  
Angular Distortion ◽  
Equivalent Stiffness ◽  
Distribution Of The Maximum ◽  
Bias Factor ◽  
Total Settlement ◽  
Design Requirements

The serviceability limit state (SLS) design of foundations typically proceeds by limiting the total settlement of individual foundations and thereby attempting to restrict the differential settlement between pairs of foundations. Due to the uncertain nature of the supporting ground, the magnitude of settlement and differential settlement are random. As it is often the differential settlement which governs serviceability, it is desirable to provide design requirements which suitably restrict differential settlements. This paper investigates, by Monte Carlo simulation, the distribution of the maximum differential settlement between pairs of foundations as a function of the spacing between foundations and the number of foundations – groups of 4, 9, or 16 foundations, arranged on a grid, are considered. The effects of the correlations between the equivalent stiffness of the ground under each foundation, as well as between the loads applied to the foundations, on the distribution of the maximum differential settlements and angular distortions are investigated. Ratios of resistance factor to resistance bias factor are presented that can be used to calibrate design requirements on the total settlement of individual foundations which also simultaneously achieve acceptable performance with respect to angular distortion.

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