scholarly journals Forced response characteristics of random mistuned blade disk based on weibull distribution and monte carlo simulation

2019 ◽  
Vol 21 (6) ◽  
pp. 1600-1612
Author(s):  
Hongyuan Zhang ◽  
Huiqun Yuan ◽  
Hongyun Sun
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Weibull Distribution ◽  
Forced Response ◽  
Response Characteristics

Gas Turbine Safety Improvement Through Risk Analysis

1988 ◽  
Vol 110 (2) ◽  
pp. 265-270 ◽  
Author(s):  
T. M. Crosby ◽  
G. L. Reinman
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Risk Analysis ◽  
Weibull Distribution ◽  
Gas Turbine ◽  
System Model ◽  
Weibull Analysis ◽  
System Safety ◽  
Weibull Plot ◽  
Safety Improvement

This paper is intended to provide the engineer with the information necessary to understand certain statistical methods that are used to improve system safety. It will provide an understanding of Weibull analysis, in that it describes when the Weibull distribution is appropriate, how to construct a Weibull plot, and how to use the parameters of the Weibull distribution to calculate risk. The paper will also provide the engineer with a comprehension of Monte Carlo simulation as it relates to quantifying safety risk. The basic components of Monte Carlo simulation are discussed as well as the formulation of a system model and its application in the gas turbine industry.

Influence of Applied Tensile and Bending Strains on Local and Overall Critical Current of Multifilamentary Bi2223-Composite Superconductor

2007 ◽  
Vol 539-543 ◽  
pp. 739-744
Author(s):  
Shojiro Ochiai ◽  
D. Doko ◽  
Hiroshi Okuda ◽  
Sang Soo Oh ◽  
Dong Woo Ha ◽  
...  
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Distribution Function ◽  
Weibull Distribution ◽  
Critical Current ◽  
Experimental Result ◽  
N Value ◽  
Local Current ◽  
Composite Superconductor ◽  
Extent Of Damage

Influence of applied tensile and bending strains on the local and overall transport critical current Ic and n-value at 77 K of multifilamentary Bi2223-composite superconductor was studied, where the n-value refers to the sharpness of the transition from super- to normal conducting state. Under both tensile and bending strains, the damage such as transverse and longitudinal cracking of the Bi2223 filaments and interfacial debonding between the filament and silver progressed. The extent of damage and accordingly the critical current was different among the local portions. The relation of the local current and n-value to overall ones was analyzed with a voltage summation model, with which the experimental result was described well. Further analysis revealed that the distribution of local critical current could be described by the Weibull distribution function and n-value could be expressed as a function of critical current. Based on these results, a Monte Carlo simulation was carried out to predict the overall critical current from the distribution of local critical current, with which the experimental results could be described.

Failure rate analysis of jaw crusher using Weibull model

2016 ◽  
Vol 231 (4) ◽  
pp. 760-772 ◽  
Author(s):  
RS Sinha ◽  
AK Mukhopadhyay
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Likelihood Estimation ◽  
Jaw Crusher ◽  
Two Parameter

The primary crusher is essential equipment employed for comminuting the mineral in processing plants. Any kind of failure of its components will accordingly hinder the performance of the plant. Therefore, to minimize sudden failures, analysis should be undertaken to improve performance and operational reliability of the crushers and its components. This paper considers the methods for analyzing failure rates of a jaw crusher and its critical components application of a two-parameter Weibull distribution in a mineral processing plant fitted using statistical tests such as goodness of fit and maximum likelihood estimation. Monte Carlo simulation, analysis of variance, and artificial neural network are also applied. Two-parameter Weibull distribution is found to be the best fit distribution using Kolmogorov–Smirnov test. Maximum likelihood estimation method is used to find out the shape and scale parameter of two-parameter Weibull distribution. Monte Carlo simulation generates 40 numbers of shape parameters, scale parameters, and time. Further, 40 numbers of Weibull distribution parameters are evaluated to examine the failure rate, significant difference, and regression coefficient using ANOVA. Artificial neural network with back-propagation algorithm is used to determine R2 and is compared with analysis of variance.

Systematic Mistuning of Bladed Disk Assemblies With Friction Contacts

2004 ◽  
Author(s):  
Florian Go¨tting ◽  
Walter Sextro ◽  
Lars Panning ◽  
Karl Popp
Keyword(s):  
Monte Carlo ◽  
Weibull Distribution ◽  
Approximate Method ◽  
Natural Frequencies ◽  
Forced Response ◽  
Mean Values ◽  
Friction Dampers ◽  
System Parameters ◽  
Bladed Disk ◽  
Standard Deviations

In turbomachinery, friction contacts are widely used to reduce dynamic stresses in turbine blades in order to avoid expensive damages. As a result of energy dissipation in the friction contacts the blade vibration amplitudes are reduced. In case of so-called friction dampers, which are pressed on the platforms of the blades by centrifugal forces, the damping effect can be optimized by varying the damper mass. This optimization can be done by means of a simulation model applying the so-called component mode synthesis and the Harmonic Balance Method to reduce computation time. It is based on the modal description of each substructure. In a real turbine or compressor blading great differences in the magnitude of the individual blade amplitudes occur caused by unavoidable mistuning of all system parameters like contact parameters and natural frequencies of the blades. It may happen that most of the blades experience only small stresses whereas a few blades experience critical stresses. Therefore, it is necessary to consider mistuning for all system parameters to simulate the forced response of bladed disk assemblies with friction contacts. For a mistuned bladed disk the complete system has to be modeled to calculate the dynamic response. In practice, usually the standard deviations instead of the distributions of the system parameters are known. Therefore, Monte-Carlo simulations are necessary to calculate the forced response of the blades for given mean values and standard deviations of the system parameters. To reduce the computational time, an approximate method has been developed and extended for small and moderate standard deviations of the system parameters to calculate the distribution and the envelopes of the frequency response functions for statistically varying system parameters, in the following called statistical mistuning. The approximate method is based on a sensitivity analysis and the assumption of a Weibull distribution of the vibration amplitudes of the blades. Both, the approximate method and the assumption of a Weibull distribution of the vibration amplitudes are validated by Monte-Carlo simulations. By these investigations the influence of different arrangements of the system parameters for given mean values and standard deviations of the vibration amplitudes of the blades can be determined, too. For the present investigations only a small influence of the arrangement of blades with respect to their natural frequencies has been observed. On the other hand, an intentional mistuning of the damper masses and the natural frequencies of the blades in a systematic way, in the following called systematic mistuning, can be investigated to reduce the amplitudes of the system. The simulation results of a systematic mistuning has been validated by a test rig with a rotating bladed disk assembly with friction dampers. The investigations show a good agreement between the simulations and the measurements but only a slight decrease of the maximum amplitudes in case of a systematic mistuning.

Computational Techniques for Probabilistic Analysis of Turbomachinery

1992 ◽  
Author(s):  
H. R. Millwater ◽  
A. J. Smalley ◽  
Y.-T. Wu ◽  
T. Y. Torng ◽  
B. F. Evans
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Importance Sampling ◽  
Probabilistic Analysis ◽  
Sampling Methods ◽  
Forced Response ◽  
Cumulative Distribution ◽  
Computational Techniques ◽  
Response Analysis ◽  
Transmitted Force

This paper reports on some advanced computational techniques for probabilistic analysis of turbomachinery. A description of the requirements for probabilistic analysis and several solution methods are summarized. The traditional probabilistic analysis method, Monte Carlo simulation, and two advanced techniques, the Advanced Mean Value (AMV) method and importance sampling, are discussed. The performance of the Monte Carlo, AMV, and importance sampling methods is explored through a forced response analysis of a two degree-of-freedom Jeffcott rotor model. Variations in rotor weight, shaft length, shaft diameter, Young’s modulus, foundation stiffness, bearing clearance, viscosity, and length are considered. The cumulative distribution function of transmitted force is computed using Monte Carlo simulation and AMV at several RPM. Also, importance sampling is used to compute the probability of transmitted force exceeding a specified limit at several RPM. In both cases, the AMV and importance sampling methods are shown to give accurate solutions with far fewer number of simulations than the Monte Carlo method. These methods enable the engineer to perform accurate and efficient probabilistic analysis of realistic complex rotor dynamic models.

scholarly journals Maximum logq Likelihood Estimation for Parameters of Weibull Distribution and Properties: Monte Carlo Simulation

2021 ◽  
Author(s):  
Mehmet Niyazi Cankaya ◽  
Roberto Vila
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Weibull Distribution ◽  
Mean Squared Error ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Likelihood Method ◽  
P Value ◽  
Test Statistic ◽  
Log Likelihood

Abstract The maximum logq likelihood estimation method is a generalization of the known maximum log likelihood method to overcome the problem for modeling non-identical observations ( inliers and outliers). The parameter $q$ is a tuning constant to manage the modeling capability. Weibull is a flexible and popular distribution for problems in engineering. In this study, this method is used to estimate the parameters of Weibull distribution when non-identical observations exist. Since the main idea is based on modeling capability of objective function p(x; ʘ) = logq [f(x; ʘ)], we observe that the finiteness of score functions cannot play a role in the robust estimation for inliers . The properties of Weibull distribution are examined. In the numerical experiment, the parameters of Weibull distribution are estimated by logq and its special form, log , likelihood methods if the different designs of contamination into underlying Weibull distribution are applied. The optimization is performed via genetic algorithm. The modeling competence of p(x; ʘ) and insensitiveness to non-identical observations are observed by Monte Carlo simulation. The value of $q$ can be chosen by use of the mean squared error in simulation and the $p$ -value of Kolmogorov - Smirnov test statistic used for evaluation of fitting competence. Thus, we can overcome the problem about determining of the value of $q$ for real data sets.

scholarly journals Parameter Estimation of Weibull Distribution Based on Second-Kind Statistics

2010 ◽  
Vol 6 (3) ◽  
pp. 109 ◽  
Author(s):  
Zengguo Sun ◽  
Chongzhao Han
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Parameter Estimation ◽  
Weibull Distribution ◽  
Closed Form ◽  
Synthetic Aperture ◽  
Sar Image ◽  
Moment Estimator ◽  
Computationally Efficient ◽  
The Moment

The log-cumulant estimator is proposed to estimate the parameters of Weibull distribution based on second-kind statistics. With the explicit closed form expressions, the log-cumulant estimator is computationally efficient. Parameterestimation results from Monte Carlo simulation and real synthetic aperture radar (SAR) image demonstrate that the log-cumulant estimator leads to better performance when compared to the moment estimator.

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