Characterization of Structural Dynamics With Uncertainty by Using Gaussian Processes

2011 ◽  
Author(s):  
Z. Xia ◽  
J. Tang
Keyword(s):  
Gaussian Process ◽  
Gaussian Processes ◽  
Regression Models ◽  
Structural Response ◽  
Gaussian Process Regression ◽  
Monte Carlo Sampling ◽  
Structural Systems ◽  
Data Points ◽  
Small Set

An efficient way to capture the dynamic characteristics of structural systems with uncertainties has been an important and challenging subject. While such characterization is valuable for structural response predictions, it could be impractical in many application situations where a sufficiently large sample is expensive or unavailable. In this paper, Gaussian process regression models are employed to capture structural dynamical responses, especially responses with uncertainties. When Gaussian processes are used to make predictions for responses with uncertainties, the sampling costs can be significantly reduced because only a relatively small set of data points is needed. With no loss of generality, applications of Gaussian process regression models are introduced in conjunction with Monte Carlo sampling. This approach can be easily generalized to situations where data points are obtained by other sampling techniques.

Minimal distributions in a stochastic partial ordering and bounds for Gaussian processes

1983 ◽  
Vol 20 (03) ◽  
pp. 529-536
Author(s):  
W. J. R. Eplett
Keyword(s):  
Gaussian Process ◽  
Gaussian Processes ◽  
Partial Ordering ◽  
Boundary Crossing ◽  
Conditional Probabilities ◽  
Life Distribution ◽  
Life Distributions ◽  
Bounded Below ◽  
Crossing Probabilities

A natural requirement to impose upon the life distribution of a component is that after inspection at some randomly chosen time to check whether it is still functioning, its life distribution from the time of checking should be bounded below by some specified distribution which may be defined by external considerations. Furthermore, the life distribution should ideally be minimal in the partial ordering obtained from the conditional probabilities. We prove that these specifications provide an apparently new characterization of the DFRA class of life distributions with a corresponding result for IFRA distributions. These results may be transferred, using Slepian's lemma, to obtain bounds for the boundary crossing probabilities of a stationary Gaussian process.

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.

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.

Validation of Adaptive Gaussian Process Regression Model Used for SIF Prediction

2018 ◽  
Author(s):  
Arvind Keprate ◽  
R. M. Chandima Ratnayake ◽  
Shankar Sankararaman
Keyword(s):  
Regression Model ◽  
Gaussian Process ◽  
Prediction Accuracy ◽  
Experimental Validation ◽  
Gaussian Process Regression ◽  
Absolute Error ◽  
Coefficient Of Determination ◽  
Data Sets ◽  
Maximum Absolute Error ◽  
Data Points

The main aim of this paper is to perform the validation of the adaptive Gaussian process regression model (AGPRM) developed by the authors for the Stress Intensity Factor (SIF) prediction of a crack propagating in topside piping. For validation purposes, the values of SIF obtained from experiments available in the literature are used. Sixty-six data points (consisting of L, a, c and SIF values obtained by experiments) are used to train the AGPRM, while four independent data sets are used for validation purposes. The experimental validation of the AGPRM also consists of the comparison of the prediction accuracy of AGPRM and Finite Element Method (FEM) relative to the experimentally derived SIF values. Four metrics, namely, Root Mean Square Error (RMSE), Average Absolute Error (AAE), Maximum Absolute Error (MAE), and Coefficient of Determination (R2), are used to compare the accuracy. A case study illustrating the development and experimental validation of the AGPRM is presented. Results indicate that the prediction accuracy of the AGPRM is comparable with and even higher than that of the FEM, provided the training points of the AGPRM are aptly chosen.

scholarly journals Detecting periodicities with Gaussian processes

2016 ◽  
Vol 2 ◽  
pp. e50 ◽  
Author(s):  
Nicolas Durrande ◽  
James Hensman ◽  
Magnus Rattray ◽  
Neil D. Lawrence
Keyword(s):  
Hilbert Space ◽  
Gaussian Process ◽  
Gaussian Processes ◽  
Covariance Function ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Gaussian Process Regression ◽  
Inner Product ◽  
Input Output ◽  
Periodic Data

We consider the problem of detecting and quantifying the periodic component of a function given noise-corrupted observations of a limited number of input/output tuples. Our approach is based on Gaussian process regression, which provides a flexible non-parametric framework for modelling periodic data. We introduce a novel decomposition of the covariance function as the sum of periodic and aperiodic kernels. This decomposition allows for the creation of sub-models which capture the periodic nature of the signal and its complement. To quantify the periodicity of the signal, we derive a periodicity ratio which reflects the uncertainty in the fitted sub-models. Although the method can be applied to many kernels, we give a special emphasis to the Matérn family, from the expression of the reproducing kernel Hilbert space inner product to the implementation of the associated periodic kernels in a Gaussian process toolkit. The proposed method is illustrated by considering the detection of periodically expressed genes in thearabidopsisgenome.

scholarly journals Exploitation of Kronecker Structure in Gaussian Process Regression for Efficient Biomedical Signal Processing

2021 ◽  
Vol 7 (2) ◽  
pp. 287-290
Author(s):  
Jannik Prüßmann ◽  
Jan Graßhoff ◽  
Philipp Rostalski
Keyword(s):  
Gaussian Process ◽  
Source Separation ◽  
Gaussian Process Regression ◽  
Efficient Solutions ◽  
Biomedical Signal Processing ◽  
Hyperparameter Optimization ◽  
Performance Loss ◽  
Versatile Tool ◽  
Data Points ◽  
Spatio Temporal

Abstract Gaussian processes are a versatile tool for data processing. Unfortunately, due to storage and runtime requirements, standard Gaussian process (GP) methods are limited to a few thousand data points. Thus, they are infeasible in most biomedical, spatio-temporal problems. The methods treated in this work cover GP inference and hyperparameter optimization, exploiting the Kronecker structure of covariance matrices. To solve regression and source separation problems, two different approaches are presented. The first approach uses efficient matrix-vector-products, whilst the second approach is based on efficient solutions to the eigendecomposition. The latter also enables efficient hyperparameter optimization. In comparison to standard GP methods, the proposed methods can be applied to very large biomedical datasets without any further performance loss and perform substantially faster. The performance is demonstrated on esophageal manometry data, where the cardiac and respiratory signal components are to be inferred by source separation.

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