Gaussian Mixtures
You can download the notebook version here:
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Below you can find the overview of the tutorials.
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> Application examples
Paper Title Gaussian Mixture Model for Robust Design Optimization of Planar Steel Frames
Year 2020
Author(s) Bach Do, Makoto Ohsaki
Link https://link.springer.com/article/10.1007/s00158-020-02676-3
ML Tags
Gaussian Mixtures
Topic Tags
Structural Design
Multi-Objective Robust Design Optimization (RDO)
Multi-Objective Genetic Algorithm (MOGA)
Software & Plug-ins Used
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MATLAB R2018a Statistics and Machine Learning Toolbox for coding and training the Gaussian mixture model (GMM)
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Summary
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This paper proposes a new method for optimizing planar steel frame structures in the presence of uncertainties in material properties, external loads, and discrete design variables. The strategy employs the power of Gaussian mixture models (GMMs) to address this complex problem. Based on selected data, the GMM is trained to predict the relationship between the random input variables and their structural response. It does this by determining the joint probability distribution function.
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The foundation of the research involves using a simple regression function to predict the structural response of the variables. With this in place, a multi-objective robust design optimization (RDO) problem is defined, comprising of three important objective functions: total mass of the structure, mean and variance of maximum inter-story drift, and maximum inter-story drift. This optimization issue is solved using a multi-objective genetic algorithm that uses the trained GMM to predict the statistical values of the impact of each variable on the structural performance. The effectiveness of this approach is demonstrated through two design examples.
Paper Title An Evolving Learning Method —Growing Gaussian Mixture Regression—for Modeling Passive
Chilled Beam Systems in Buildings
Year 2022
Author(s) Liping Wang , James Braun , Sujit Dahal
Link https://www.sciencedirect.com/science/article/pii/S037877882200398X
ML Tags
Gaussian Mixtures
Growing Gaussian Mixture Regression (GGMR)
Topic Tags
​Operational Energy / Building Energy control
Software & Plug-ins Used
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EnergyPlus for model simulations
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Niagara/AX software for Living Lab simulations
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Summary
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The researchers used an evolving learning approach called growing Gaussian mixture regression (GGMR) to estimate cooling rates in passive chilled beam (PCB) systems. The method entailed using actual system measurements and data from building energy models for training, evolution, and validation. To handle differences in system functioning that extend beyond the original training data, GGMR constantly modifies important parameters such as weight coefficients, means, and covariance matrices of Gaussian components.
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The study made a strong argument for GGMR's efficacy as an evolving learning-based, data-driven strategy for precisely projecting cooling rates in PCB systems. The research also delves into the selection of crucial performance characteristics for GGMR models, such as the number of components, training data size, and learning rate.
Paper Title A visualized soundscape prediction model for design processes in urban parks
Year 2022
Author(s) Ran Yue, Qi Meng, Da Yang, Yue Wu, Fangfang Liu, Wei Yan
Link https://www.sciencedirect.com/science/article/pii/S037877882200398X
ML Tags
Gaussian Mixtures
Topic Tags
Urban Planning
Acoustics
Software & Plug-ins Used
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ArcGIS for grid division methods
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Summary
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In this study, a model is constructed to predict several features of the acoustic environment in an urban design context, such as sound pressure level (SPL), sound source location, and soundscape quality. The model uses a grid-based method and a Gaussian mixture model (GMM) in a machine learning framework to consider urban design factors.
To train the model, first data is collected. Subjective perceptual data is obtained on site using the soundwalk method in three sample urban parks. This data is then used to evaluate the model's correctness. The model is trained to predict the relationship between design factors and the resulting acoustic environment. The trained model can predict soundscape quality, and displaying the prediction results by combining geographic, visual, and auditory data.
The soundscape prediction is particularly relevant in the context of urban planning. The model's output enables users to quickly compare the trade-off between different urban park design features and their impact on the resulting acoustic environment. The study also proposes specific optimization techniques for improving the soundscape quality in urban parks based on the model's simulation findings.
Paper Title Extended and Generalized Fragility Functions
Year 2018
Author(s) C. P. Andriotis and K. G. Papakonstantinou
Link https://www.researchgate.net/publication/326331208_Extended_and_Generalized_Fragility_Functions
ML Tags
Gaussian Mixtures
dependent Markov Decision Processes
Hidden Markov Decision Processes
Topic Tags
Earthquake Engineering
Seismic Design
Software & Plug-ins Used
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MATLAB for generalized fragility functions
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Summary
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This paper describes fragility functions and aims to create fragility functions that are exceptionally comprehensive. These fragility functions take into consideration two essential aspects: (1) using multivariate intensity measurements with different damage states, and (2) accounting for the time dependencies of longitudinal damage state.
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The first part of the paper introduces fragility functions and how they give a complete picture fragility. The second part introduces the authors’ work of creating “generalized fragility functions" which can handle a much larger number of states. These functions are intended to handle scenarios where many transitions between system states must be captured. Dependent Markov and hidden Markov models are used to correctly capture these transitions.
The paper offers numerical results as well as extensive insights into their implementation, statistical features, and practical advice to help in the efficient use of these fragility functions.