Multiscale Topology Optimization With Gaussian Process Regression Models

2021 ◽  
Author(s):  
Joel C. Najmon ◽  
Homero Valladares ◽  
Andres Tovar
Keyword(s):  
Topology Optimization ◽  
Gaussian Process ◽  
Regression Models ◽  
Computational Cost ◽  
Gaussian Process Regression ◽  
Analytical Sensitivity ◽  
Inverse Homogenization ◽  
Discrete Location ◽  
Unit Cells ◽  
Periodic Microstructures

Abstract Multiscale topology optimization (MSTO) is a numerical design approach to optimally distribute material within coupled design domains at multiple length scales. Due to the substantial computational cost of performing topology optimization at multiple scales, MSTO methods often feature subroutines such as homogenization of parameterized unit cells and inverse homogenization of periodic microstructures. Parameterized unit cells are of great practical use, but limit the design to a pre-selected cell shape. On the other hand, inverse homogenization provide a physical representation of an optimal periodic microstructure at every discrete location, but do not necessarily embody a manufacturable structure. To address these limitations, this paper introduces a Gaussian process regression model-assisted MSTO method that features the optimal distribution of material at the macroscale and topology optimization of a manufacturable microscale structure. In the proposed approach, a macroscale optimization problem is solved using a gradient-based optimizer The design variables are defined as the homogenized stiffness tensors of the microscale topologies. As such, analytical sensitivity is not possible so the sensitivity coefficients are approximated using finite differences after each microscale topology is optimized. The computational cost of optimizing each microstructure is dramatically reduced by using Gaussian process regression models to approximate the homogenized stiffness tensor. The capability of the proposed MSTO method is demonstrated with two three-dimensional numerical examples. The correlation of the Gaussian process regression models are presented along with the final multiscale topologies for the two examples: a cantilever beam and a 3-point bending beam.

Structured Gaussian Process Regression of Music Mood

2020 ◽  
Vol 176 (2) ◽  
pp. 183-203
Author(s):  
Santosh Chapaneri ◽  
Deepak Jayaswal
Keyword(s):  
Gaussian Process ◽  
Computational Cost ◽  
Gaussian Process Regression ◽  
Gaussian Mixture ◽  
Feature Representation ◽  
Affective Content ◽  
Variational Bayesian Inference ◽  
Benchmark Datasets ◽  
Valence And Arousal ◽  
Structured Regression

Modeling the music mood has wide applications in music categorization, retrieval, and recommendation systems; however, it is challenging to computationally model the affective content of music due to its subjective nature. In this work, a structured regression framework is proposed to model the valence and arousal mood dimensions of music using a single regression model at a linear computational cost. To tackle the subjectivity phenomena, a confidence-interval based estimated consensus is computed by modeling the behavior of various annotators (e.g. biased, adversarial) and is shown to perform better than using the average annotation values. For a compact feature representation of music clips, variational Bayesian inference is used to learn the Gaussian mixture model representation of acoustic features and chord-related features are used to improve the valence estimation by probing the chord progressions between chroma frames. The dimensionality of features is further reduced using an adaptive version of kernel PCA. Using an efficient implementation of twin Gaussian process for structured regression, the proposed work achieves a significant improvement in R2 for arousal and valence dimensions relative to state-of-the-art techniques on two benchmark datasets for music mood estimation.

Gaussian Process Regression Models for the Prediction of Hydrogen Bond Acceptor Strengths

2018 ◽  
Vol 38 (4) ◽  
pp. 1800115 ◽  
Author(s):  
Christoph A. Bauer ◽  
Gisbert Schneider ◽  
Andreas H. Göller
Keyword(s):  
Hydrogen Bond ◽  
Gaussian Process ◽  
Regression Models ◽  
Gaussian Process Regression ◽  
Hydrogen Bond Acceptor

scholarly journals A Vision-Based Approach for Sidewalk and Walkway Trip Hazards Assessment

2020 ◽  
Vol 17 (22) ◽  
pp. 8438
Author(s):  
Rachel Cohen ◽  
Geoff Fernie ◽  
Atena Roshan Fekr
Keyword(s):  
Environmental Factors ◽  
Edge Detection ◽  
Gaussian Process ◽  
Regression Models ◽  
Gaussian Process Regression ◽  
Region Growing ◽  
Cost Effective ◽  
Second Phase ◽  
Cost Effective Method ◽  
Regression Techniques

Tripping hazards on the sidewalk cause many falls annually, and the inspection and repair of these hazards cost cities millions of dollars. Currently, there is not an efficient and cost-effective method to monitor the sidewalk to identify any possible tripping hazards. In this paper, a new portable device is proposed using an Intel RealSense D415 RGB-D camera to monitor the sidewalks, detect the hazards, and extract relevant features of the hazards. This paper first analyzes the effects of environmental factors contributing to the device’s error and compares different regression techniques to calibrate the camera. The Gaussian Process Regression models yielded the most accurate predictions with less than 0.09 mm Mean Absolute Errors (MAEs). In the second phase, a novel segmentation algorithm is proposed that combines the edge detection and region-growing techniques to detect the true tripping hazards. Different examples are provided to visualize the output results of the proposed method.

Topology Optimization of Periodic Structures With Substructuring

2019 ◽  
Vol 141 (7) ◽  
Author(s):  
Junjian Fu ◽  
Liang Xia ◽  
Liang Gao ◽  
Mi Xiao ◽  
Hao Li
Keyword(s):  
Topology Optimization ◽  
Linear System ◽  
Periodic Structures ◽  
Computational Cost ◽  
Optimization Method ◽  
Displacement Fields ◽  
Element Analysis ◽  
Level Set Function ◽  
Static Condensation ◽  
Unit Cells

Topology optimization of macroperiodic structures is traditionally realized by imposing periodic constraints on the global structure, which needs to solve a fully linear system. Therefore, it usually requires a huge computational cost and massive storage requirements with the mesh refinement. This paper presents an efficient topology optimization method for periodic structures with substructuring such that a condensed linear system is to be solved. The macrostructure is identically partitioned into a number of scale-related substructures represented by the zero contour of a level set function (LSF). Only a representative substructure is optimized for the global periodic structures. To accelerate the finite element analysis (FEA) procedure of the periodic structures, static condensation is adopted for repeated common substructures. The macrostructure with reduced number of degree of freedoms (DOFs) is obtained by assembling all the condensed substructures together. Solving a fully linear system is divided into solving a condensed linear system and parallel recovery of substructural displacement fields. The design efficiency is therefore significantly improved. With this proposed method, people can design scale-related periodic structures with a sufficiently large number of unit cells. The structural performance at a specified scale can also be calculated without any approximations. What’s more, perfect connectivity between different optimized unit cells is guaranteed. Topology optimization of periodic, layerwise periodic, and graded layerwise periodic structures are investigated to verify the efficiency and effectiveness of the presented method.

scholarly journals Parameterization of wind evolution using lidar

2021 ◽  
Vol 6 (1) ◽  
pp. 61-91
Author(s):  
Yiyin Chen ◽  
David Schlipf ◽  
Po Wen Cheng
Keyword(s):  
Gaussian Process ◽  
Wind Field ◽  
Regression Models ◽  
Gaussian Process Regression ◽  
Evolution Model ◽  
Model Parameters ◽  
Turbulence Structures ◽  
Wind Turbine Control ◽  
Automatic Relevance Determination ◽  
Control Concept

Abstract. Wind evolution, i.e., the evolution of turbulence structures over time, has become an increasingly interesting topic in recent years, mainly due to the development of lidar-assisted wind turbine control, which requires accurate prediction of wind evolution to avoid unnecessary or even harmful control actions. Moreover, 4D stochastic wind field simulations can be made possible by integrating wind evolution into standard 3D simulations to provide a more realistic simulation environment for this control concept. Motivated by these factors, this research aims to investigate the potential of Gaussian process regression in the parameterization of wind evolution. Wind evolution is commonly quantified using magnitude-squared coherence of wind speed and is estimated with lidar data measured by two nacelle-mounted lidars in this research. A two-parameter wind evolution model modified from a previous study is used to model the estimated coherence. A statistical analysis is done for the wind evolution model parameters determined from the estimated coherence to provide some insights into the characteristics of wind evolution. Gaussian process regression models are trained with the wind evolution model parameters and different combinations of wind-field-related variables acquired from the lidars and a meteorological mast. The automatic relevance determination squared exponential kernel function is applied to select suitable variables for the models. The performance of the Gaussian process regression models is analyzed with respect to different variable combinations, and the selected variables are discussed to shed light on the correlation between wind evolution and these variables.

Data-Driven Multiscale Topology Optimization Using Multi-Response Latent Variable Gaussian Process

2020 ◽  
Author(s):  
Liwei Wang ◽  
Siyu Tao ◽  
Ping Zhu ◽  
Wei Chen
Keyword(s):  
Topology Optimization ◽  
Gaussian Process ◽  
Latent Variable ◽  
Distance Measure ◽  
Material Design ◽  
Cell Types ◽  
Unit Cell ◽  
Data Driven ◽  
Single Class ◽  
Unit Cells

Abstract The data-driven approach is emerging as a promising method for the topological design of the multiscale structure with greater efficiency. However, existing data-driven methods mostly focus on a single class of unit cells without considering multiple classes to accommodate spatially varying desired properties. The key challenge is the lack of inherent ordering or “distance” measure between different classes of unit cells in meeting a range of properties. To overcome this hurdle, we extend the newly developed latent-variable Gaussian process (LVGP) to creating multi-response LVGP (MRLVGP) for the unit cell libraries of metamaterials, taking both qualitative unit cell concepts and quantitative unit cell design variables as mixed-variable inputs. The MRLVGP embeds the mixed variables into a continuous design space based on their collective effect on the responses, providing substantial insights into the interplay between different geometrical classes and unit cell materials. With this model, we can easily obtain a continuous and differentiable transition between different unit cell concepts that can render gradient information for multiscale topology optimization. While the proposed approach has a broader impact on the concurrent topological and material design of engineered systems, we demonstrate its benefits through multiscale topology optimization with aperiodic unit cells. Design examples reveal that considering multiple unit cell types can lead to improved performance due to the consistent load-transferred paths for micro- and macrostructures.

Gaussian Process Regression hyperparameter optimization for image time series gap-filling of Earth observation data and crop monitoring

2021 ◽  
Author(s):  
Santiago Belda ◽  
Matías Salinero ◽  
Eatidal Amin ◽  
Luca Pipia ◽  
Pablo Morcillo-Pallarés ◽  
...  
Keyword(s):  
Time Series ◽  
Gaussian Process ◽  
Computational Cost ◽  
Gaussian Process Regression ◽  
Superior Performance ◽  
Observation Data ◽  
Gap Filling ◽  
Crop Monitoring ◽  
Exponential Kernel ◽  
Uncertainty Estimates

<p>In general, modeling phenological evolution represents a challenging task mainly because of time series gaps and noisy data, coming from different viewing and illumination geometries, cloud cover, seasonal snow and the interval needed to revisit and acquire data for the exact same location. For that reason, the use of reliable gap-filling fitting functions and smoothing filters is frequently required for retrievals at the highest feasible accuracy. Of specific interest to filling gaps in time series is the emergence of machine learning regression algorithms (MLRAs) which can serve as fitting functions. Among the multiple MLRA approaches currently available, the kernel-based methods developed in a Bayesian framework deserve special attention because of both being adaptive and providing associated uncertainty estimates, such as Gaussian Process Regression (GPR).</p><p>Recent studies demonstrated the effectiveness of GPR for gap-filling of biophysical parameter time series because the hyperparameters can be optimally set for each time series (one for each pixel in the area) with a single optimization procedure. The entire procedure of learning a GPR model only relies on appropriate selection of the type of kernel and the hyperparameters involved in the estimation of input data covariance. Despite its clear strategic advantage, the most important shortcomings of this technique are the (1) high computational cost and (2) memory requirements of their training, which grows cubically and quadratically with the number of model’s samples, respectively. This can become problematic in view of processing a large amount of data, such as in Sentinel-2 (S2) time series tiles. Hence, optimization strategies need to be developed on how to speed up the GPR processing while maintaining the superior performance in terms of accuracy.</p><p>To mitigate its computational burden and to address such shortcoming and repetitive procedure, we evaluated whether the GPR hyperparameters can be preoptimized over a reduced set of representative pixels and kept fixed over a more extended crop area. We used S2 LAI time series over an agricultural region in Castile and Leon (North-West Spain) and testing different functions for Covariance estimation such as exponential Kernel, Squared exponential kernel and matern kernel with parameter 3/2 or 5/2. The performance of image reconstructions was compared against the standard per-pixel GPR time series training process. Results showed that accuracies were on the same order (12% RMSE degradation) whereas processing time accelerated up to 90 times. Crop phenology indicators were also calculated and compared, revealing similar temporal patterns with differences in start and end of growing season of no more than five days. To the benefit of crop monitoring applications, all the gap-filling and phenology indicators retrieval techniques have been implemented into the <strong>freely downloadable GUI toolbox DATimeS</strong> (Decomposition and Analysis of Time Series Software - https://artmotoolbox.com/).</p>

scholarly journals Application of Gaussian process regression models for capturing the evolution of microstructure statistics in aging of nickel-based superalloys

2019 ◽  
Vol 178 ◽  
pp. 45-58 ◽  
Author(s):  
Yuksel C. Yabansu ◽  
Almambet Iskakov ◽  
Anna Kapustina ◽  
Sudhir Rajagopalan ◽  
Surya R. Kalidindi
Keyword(s):  
Gaussian Process ◽  
Regression Models ◽  
Gaussian Process Regression ◽  
Evolution Of Microstructure
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