ANALYSIS OF EARTHQUAKE MOTION USING THE KERNEL DENSITY ESTIMATION AND GAUSSIAN MIXTURE MODEL

Author(s):  
Masumitsu KUSE ◽  
Nobuoto NOJIMA
2013 ◽  
Vol 380-384 ◽  
pp. 1394-1397
Author(s):  
Hong Hai Liu ◽  
Xiang Hua Hou

When modeling background model by Gaussian mixture model, there exist the defects that parameters can not be updated adaptively. In this paper, we adopt mean-shift algorithm to overcome these defects. Firstly, this paper introduces the initialized parameters, such as variance, mean, and weights and others, when modeling and then the parameters are constantly adjusted in the subsequent calculations. Then the statistical background model based on probability density estimation is put forward and using mean-shift algorithm updates the parameters adaptively. At last, the algorithm of mixture Gaussian background modeling method based on mean-shift is implemented. The experimental results show that the algorithm can effectively update parameters adaptively and the obtained background model is better.


2022 ◽  
Author(s):  
Xiaodong Zhang ◽  
Anand Natarajan

Abstract. Uncertainty quantification is a necessary step in wind turbine design due to the random nature of the environmental loads, through which the uncertainty of structural loads and responses under specific situations can be quantified. Specifically, wind turbulence has a significant impact on the extreme and fatigue design envelope of the wind turbine. The wind parameters (mean and standard deviation of 10-minute wind speed) are usually not independent, and it will lead to biased results for structural reliability or uncertainty quantification assuming the wind parameters are independent. A proper probabilistic model should be established to model the correlation among wind parameters. Compared to univariate distributions, theoretical multivariate distributions are limited and not flexible enough to model the wind parameters from different sites or direction sectors. Copula-based models are used often for correlation description, but existing parametric copulas may not model the correlation among wind parameters well due to limitations of the copula structures. The Gaussian mixture model is widely applied for density estimation and clustering in many domains, but limited studies were conducted in wind energy and few used it for density estimation of wind parameters. In this paper, the Gaussian mixture model is used to model the joint distribution of mean and standard deviation of 10-minute wind speed, which is calculated from 15 years of wind measurement time series data. As a comparison, the Nataf transformation (Gaussian copula) and Gumbel copula are compared with the Gaussian mixture model in terms of the estimated marginal distributions and conditional distributions. The Gaussian mixture model is then adopted to estimate the extreme wind turbulence, which could be taken as an input to design loads used in the ultimate design limit state of turbine structures. The wind turbulence associated with a 50-year return period computed from the Gaussian mixture model is compared with what is utilized in the design of wind turbines as given in the IEC 61400-1.


Author(s):  
Emily Esmeralda Carvajal-Camelo ◽  
Jose Bernal ◽  
Arnau Oliver ◽  
Xavier Lladó ◽  
Maria Trujillo

Atrophy quantification is fundamental for understanding brain development and diagnosing and monitoring brain diseases. FSL-SIENA is a well-known fully-automated method that has been widely used in brain magnetic resonance imaging studies. However, intensity variations arising during image acquisition that may compromise evaluation, analysis and even diagnosis. In this work, we study whether intensity standardisation can improve longitudinal atrophy quantification. We considered seven methods comprising z-score, fuzzy c-means, Gaussian mixture model, kernel density, histogram matching, white stripe, and removal of artificial voxel effects by linear regression (RAVEL). We used a total of 330 scans from two publicly-available datasets, ADNI and OASIS. In scan-rescan assessments, that measures robustness to subtle imaging variations, intensity standardisation did not compromise the robustness of FSL-SIENA significantly (p>0.1). In power analysis assessments, that measures the ability to discern between two groups of subjects, three methods led to consistent improvements in both datasets with respect to the original: fuzzy c-means, Gaussian mixture model, and kernel density estimation. Reduction in sample size using these three methods ranged from 17% to 95%. The performance of the other four methods was affected by spatial normalisation, skull stripping errors, presence of periventricular white matter hyperintensities, or tissue proportion variations over time. Our work evinces the relevance of appropriate intensity standardisation in longitudinal cerebral atrophy assessments using FSL-SIENA.


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