scholarly journals Seismic fragility of bridges: An approach coupling multiple-stripe analysis and Gaussian mixture for multicomponent structures

2021 ◽  
pp. 875529302110361
Author(s):  
Pedro Alexandre Conde Bandini ◽  
Jamie Ellen Padgett ◽  
Patrick Paultre ◽  
Gustavo Henrique Siqueira
Keyword(s):  
Statistical Tests ◽  
Gaussian Mixture Models ◽  
Gaussian Mixture ◽  
Seismic Fragility ◽  
Correlated Response ◽  
Eastern Canada ◽  
Seismic Engineering ◽  
Response Data ◽  
Demand Models ◽  
Mean Annual Frequency

An approach is developed to build multivariate probabilistic seismic demand models (PSDMs) of multicomponent structures based on the coupling of multiple-stripe analysis and Gaussian mixture models. The proposed methodology is eminently flexible in terms of adopted assumptions, and a classic highway bridge in Eastern Canada is used to present an application of the new approach and to investigate its impact on seismic fragility analysis. Traditional PSDM methods employ lognormal distribution and linear correlation between pairs of components to fit the seismic response data, which may lead to poor statistical modeling. Using ground motion records rigorously selected for the investigated site, data are generated via response history analysis, and appropriate statistical tests are then performed to show that these hypotheses are not always valid on the response data of the case-study bridge. The clustering feature of the proposed methodology allows the construction of a multivariate PSDM with refined fitting to the correlated response data, introducing low bias into the fragility functions and mean annual frequency of violating damage states, which are crucial features for decision making in the context of performance-based seismic engineering.

scholarly journals Measure of Similarity between GMMs by Embedding of the Parameter Space That Preserves KL Divergence

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 957
Author(s):  
Branislav Popović ◽  
Lenka Cepova ◽  
Robert Cep ◽  
Marko Janev ◽  
Lidija Krstanović
Keyword(s):  
Computational Complexity ◽  
Parameter Space ◽  
Recognition Accuracy ◽  
Gaussian Mixture Models ◽  
Gaussian Mixture ◽  
Dimensional Manifold ◽  
Dimensional Parameter ◽  
Trade Off ◽  
Measure Of Similarity ◽  
Lower Dimensional

In this work, we deliver a novel measure of similarity between Gaussian mixture models (GMMs) by neighborhood preserving embedding (NPE) of the parameter space, that projects components of GMMs, which by our assumption lie close to lower dimensional manifold. By doing so, we obtain a transformation from the original high-dimensional parameter space, into a much lower-dimensional resulting parameter space. Therefore, resolving the distance between two GMMs is reduced to (taking the account of the corresponding weights) calculating the distance between sets of lower-dimensional Euclidean vectors. Much better trade-off between the recognition accuracy and the computational complexity is achieved in comparison to measures utilizing distances between Gaussian components evaluated in the original parameter space. The proposed measure is much more efficient in machine learning tasks that operate on large data sets, as in such tasks, the required number of overall Gaussian components is always large. Artificial, as well as real-world experiments are conducted, showing much better trade-off between recognition accuracy and computational complexity of the proposed measure, in comparison to all baseline measures of similarity between GMMs tested in this paper.

scholarly journals A Unified Formulation of k-Means, Fuzzy c-Means and Gaussian Mixture Model by the Kolmogorov–Nagumo Average

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 518
Author(s):  
Osamu Komori ◽  
Shinto Eguchi
Keyword(s):  
Pareto Distribution ◽  
Statistical Data ◽  
Learning Algorithm ◽  
Survival Function ◽  
Gaussian Mixture Models ◽  
Gaussian Mixture ◽  
Simulation Studies ◽  
Probabilistic Framework ◽  
Underlying Distribution ◽  
Fuzzy C Means

Clustering is a major unsupervised learning algorithm and is widely applied in data mining and statistical data analyses. Typical examples include k-means, fuzzy c-means, and Gaussian mixture models, which are categorized into hard, soft, and model-based clusterings, respectively. We propose a new clustering, called Pareto clustering, based on the Kolmogorov–Nagumo average, which is defined by a survival function of the Pareto distribution. The proposed algorithm incorporates all the aforementioned clusterings plus maximum-entropy clustering. We introduce a probabilistic framework for the proposed method, in which the underlying distribution to give consistency is discussed. We build the minorize-maximization algorithm to estimate the parameters in Pareto clustering. We compare the performance with existing methods in simulation studies and in benchmark dataset analyses to demonstrate its highly practical utilities.

A robust non-rigid point set registration method based on inhomogeneous Gaussian mixture models

2017 ◽  
Vol 34 (10) ◽  
pp. 1399-1414 ◽  
Author(s):  
Wanxia Deng ◽  
Huanxin Zou ◽  
Fang Guo ◽  
Lin Lei ◽  
Shilin Zhou ◽  
...  
Keyword(s):  
Mixture Models ◽  
Gaussian Mixture Models ◽  
Gaussian Mixture ◽  
Registration Method ◽  
Point Set Registration ◽  
Point Set

Multi Object Detection and Tracking from Video File

2014 ◽  
Vol 533 ◽  
pp. 218-225 ◽  
Author(s):  
Rapee Krerngkamjornkit ◽  
Milan Simic
Keyword(s):  
Computer Vision ◽  
Background Subtraction ◽  
Moving Objects ◽  
Gaussian Mixture Models ◽  
Gaussian Mixture ◽  
Video Tracking ◽  
Partial Occlusion ◽  
Video File ◽  
Detection And Tracking ◽  
Over Time

This paper describes computer vision algorithms for detection, identification, and tracking of moving objects in a video file. The problem of multiple object tracking can be divided into two parts; detecting moving objects in each frame and associating the detections corresponding to the same object over time. The detection of moving objects uses a background subtraction algorithm based on Gaussian mixture models. The motion of each track is estimated by a Kalman filter. The video tracking algorithm was successfully tested using the BIWI walking pedestrians datasets [. The experimental results show that system can operate in real time and successfully detect, track and identify multiple targets in the presence of partial occlusion.

scholarly journals Data Assimilation with Gaussian Mixture Models Using the Dynamically Orthogonal Field Equations. Part I: Theory and Scheme

2013 ◽  
Vol 141 (6) ◽  
pp. 1737-1760 ◽  
Author(s):  
Thomas Sondergaard ◽  
Pierre F. J. Lermusiaux
Keyword(s):  
Data Assimilation ◽  
Mixture Models ◽  
Gaussian Mixture Models ◽  
Expectation Maximization Algorithm ◽  
Planck Equation ◽  
Information Criterion ◽  
Gaussian Mixture ◽  
Field Equations ◽  
Dynamical Equations ◽  
Prior Probabilities

Abstract This work introduces and derives an efficient, data-driven assimilation scheme, focused on a time-dependent stochastic subspace that respects nonlinear dynamics and captures non-Gaussian statistics as it occurs. The motivation is to obtain a filter that is applicable to realistic geophysical applications, but that also rigorously utilizes the governing dynamical equations with information theory and learning theory for efficient Bayesian data assimilation. Building on the foundations of classical filters, the underlying theory and algorithmic implementation of the new filter are developed and derived. The stochastic Dynamically Orthogonal (DO) field equations and their adaptive stochastic subspace are employed to predict prior probabilities for the full dynamical state, effectively approximating the Fokker–Planck equation. At assimilation times, the DO realizations are fit to semiparametric Gaussian Mixture Models (GMMs) using the Expectation-Maximization algorithm and the Bayesian Information Criterion. Bayes’s law is then efficiently carried out analytically within the evolving stochastic subspace. The resulting GMM-DO filter is illustrated in a very simple example. Variations of the GMM-DO filter are also provided along with comparisons with related schemes.

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