scholarly journals Statistical Investigation of Bearing Capacity of Pile Foundation Based on Bayesian Reliability Theory

2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
Zuolong Luo ◽  
Fenghui Dong
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Bearing Capacity ◽  
Normal Distribution ◽  
Pile Foundation ◽  
Maximum Likelihood Method ◽  
Forecast Model ◽  
Statistical Investigation ◽  
Likelihood Method ◽  
Estimation Accuracy

In order to improve the estimation accuracy of bearing capacity of pile foundation, a new forecast method of bearing capacity of pile foundation was proposed on Jeffrey’s noninformative prior using the MCMC (Markov chain Monte Carlo) method of the Bayesian theory. The proposed approach was used to estimate the parameters of Normal distribution. Numerical simulation was used to produce pseudosamples. The parameter estimation of the maximum likelihood method and the Bayesian statistical theory was used to estimate the parameter estimation of the Normal distribution, which has been compared with the theoretical value of the pseudosample of Normal distribution. The result indicates that the forecast model of Normal distribution using the Bayesian method is better than that of the maximum likelihood method, and the performance of the proposed method was improved with increasing of pseudosample number. At last, the proposed method was applied to estimate the parameter of Normal bearing capacity distribution of pile foundation, which shows that the proposed method has a high precision and good applicability.

Statistical evaluation of fatigue tests using maximum likelihood

2021 ◽  
Vol 63 (8) ◽  
pp. 714-720
Author(s):  
Klaus Störzel ◽  
Jörg Baumgartner
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Test Data ◽  
Maximum Likelihood Method ◽  
Statistical Evaluation ◽  
Test Procedure ◽  
Fatigue Tests ◽  
Likelihood Method ◽  
Parameter Determination ◽  
Number Of Cycles

Abstract The statistical evaluation of fatigue tests can be carried out using the maximum likelihood method. With this method, the influence of run-outs on the S-N curve can be statistically considered. Typically, a bilinear S-N curve (Wöhler curve) in double-logarithmic representation is used. The logarithmic normal distribution is the basis for describing the scatter, which is assumed here to be independent of the number of cycles. For parameter determination via the maximum likelihood method, reliability is examined and compared with the evaluation methods proposed in DIN 50100. While a defined test procedure is required for the application of DIN 50100, any test data can be evaluated according to the maximum likelihood method. In comparison with the methods proposed in DIN 50100, it could be shown through some examples that the maximum likelihood method yields very reliable results for all S-N curve parameters.

Optimization of Parameters Estimation for Normal Distribution Based on Bootstrap Method

2011 ◽  
Vol 52-54 ◽  
pp. 546-549
Author(s):  
Shi Bo Xin
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Maximum Likelihood Method ◽  
Simulation Analysis ◽  
Bootstrap Method ◽  
Parameters Estimation ◽  
Likelihood Method ◽  
Sample Mean ◽  
Optimization Of Parameters

According to sample mean submits normal distribution which is extracted from normal distribution, we give the equation of parameters estimation for normal distribution by bootstrap method, then we make a simulation analysis and compare the effect of parameters estimation which uses traditional maximum likelihood method and bootstrap method.

Application of differential evolution for wind speed distribution parameters estimation

2021 ◽  
pp. 0309524X2199996
Author(s):  
Rajesh Kumar ◽  
Arun Kumar
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Wind Speed ◽  
Weibull Distribution ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Speed Distribution ◽  
De Algorithm ◽  
Wind Speed Distribution ◽  
Distribution Parameters

Weibull distribution is an extensively used statistical distribution for analyzing wind speed and determining energy potential studies. Estimation of the wind speed distribution parameter is essential as it significantly affects the success of Weibull distribution application to wind energy. Various estimation methods viz. graphical method, moment method (MM), maximum likelihood method (ML), modified maximum likelihood method, and energy pattern factor method or power density method have been presented in various reported research studies for accurate estimation of distribution parameters. ML is the most preferred approach to study the parameter estimation. ML works on the principle of forming a likelihood function and maximizing the function for parameter estimation. ML generally uses the numerical based iterative method, such as Newton–Raphson. However, the iterative methods proposed in the literature are generally computationally intensive. In this paper, an efficient technique utilizing differential evolution (DE) algorithm to enhance the estimation accuracy of maximum likelihood estimation has been presented. The [Formula: see text] of GA-Weibull, SA-Weibull, and DE-Weibull is 0.958, 0.953, and 0.973 respectively, and value of RMSE of DE-Weibull 0.0083, GA-Weibull (0.0104), and SA-Weibull (0.0110), for the yearly wind speed data are obtained. The lowest root mean square error and larger regression value for both monthly and yearly wind speed data indicate that the DE-Weibull distribution has the best goodness of fit and advocate the DE algorithm for the parameter estimation.

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