Comparative Study of Kriging and Support Vector Regression for Structural Engineering Applications

Moustapha, Maliki; Bourinet, Jean‐Marc; Guillaume, Benoît; Sudret, Bruno

doi:10.1061/ajrua6.0000950

Cited by 47 publications

(28 citation statements)

References 48 publications

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“…GPs are often used to solve regression problems [34,35,36]. In general, regression problems are concerned with the estimation of values of a dependent variable g( ) observed at certain values of an independent variable , given a set of noisy measurements y.…”

Section: Gaussian Process Regressionmentioning

confidence: 99%

“…• Finally, the transfer function model is converted into an equivalent SSM driven by a scalar-valued white noise process with spectral density σ w Many GPs having stationary covariance functions can be expressed into state-space form as in Equation 36 with model matrices defined by F cf , L cf , H, σ w and P cf 0 . It should be noted that non-stationary covariance functions can also be converted into state-space forms [42], however the Fourier transform approach is no longer applicable.…”

Section: State Space Representation Of Temporal Gpsmentioning

confidence: 99%

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A Gaussian process latent force model for joint input-state estimation in linear structural systems

Nayek

Chakraborty

Narasimhan

2019

Mechanical Systems and Signal Processing

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The problem of combined state and input estimation of linear structural systems based on measured responses and a priori knowledge of structural model is considered. A novel methodology using Gaussian process latent force models is proposed to tackle the problem in a stochastic setting. Gaussian process latent force models (GPLFMs) are hybrid models that combine differential equations representing a physical system with data-driven non-parametric Gaussian process models. In this work, the unknown input forces acting on a structure are modelled as Gaussian processes with some chosen covariance functions which are combined with the mechanistic differential equation representing the structure to construct a GPLFM. The GPLFM is then conveniently formulated as an augmented stochastic state-space model with additional states representing the latent force components, and the joint input and state inference of the resulting model is implemented using Kalman filter. The augmented state-space model of GPLFM is shown as a generalization of the class of input-augmented state-space models, is proven observable, and is robust compared to conventional augmented formulations in terms of numerical stability. The hyperparameters governing the covariance functions are estimated using maximum likelihood optimization based on the observed data, thus overcoming the need for manual tuning of the hyperparameters by trial-and-error. To assess the performance of the proposed GPLFM method, several cases of state and input estimation are demonstrated using numerical simulations on a 10-dof shear building and a 76-storey ASCE benchmark office tower. Results obtained indicate the superior performance of the proposed approach over conventional Kalman filter based approaches.

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Section: Gaussian Process Regressionmentioning

confidence: 99%

Section: State Space Representation Of Temporal Gpsmentioning

confidence: 99%

A Gaussian process latent force model for joint input-state estimation in linear structural systems

Nayek

Chakraborty

Narasimhan

2019

Mechanical Systems and Signal Processing

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“…Many types of surrogate models, including Polynomial Chaos Expansions [8], Support Vector Machines [9], Neural Networks [10], and many other techniques have been introduced and applied in recent years.…”

Section: Introductionmentioning

confidence: 99%

On the Robust Estimation of Small Failure Probabilities for Strong Nonlinear Models

Faes

Sadeghi

Broggi

et al. 2019

ASCE-ASME J Risk and Uncert in Engrg Sys Part B Mech Engrg

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Structural reliability methods are nowadays a cornerstone for the design of robustly performing structures, thanks to advancements in modeling and simulation tools. Monte Carlo-based simulation tools have been shown to provide the necessary accuracy and flexibility. While standard Monte Carlo estimation of the probability of failure is not hindered in its applicability by approximations or limiting assumptions, it becomes computationally unfeasible when small failure probability needs to be estimated, especially when the underlying numerical model evaluation is time consuming. In this case, variance reduction techniques are commonly employed, allowing for the estimation of small failure probabilities with a reduced number of samples and model calls. As a competing approach to variance reduction techniques, surrogate models can be used to substitute the computationally expensive model and performance function with an easy to evaluate numerical function calibrated through a supervised learning procedure. Both these tools provide accurate results for structural application. However, particular care should be taken into account when the reliability problems deal with high-dimensional or strongly nonlinear structural performances since the accuracy of the estimate is largely dependent on choices made during the surrogate modeling process. In this work, we compare the performance of the most recent state-of-the-art advance Monte Carlo techniques and surrogate models when applied to strongly nonlinear performance functions. This will provide the analysts with an insight to the issues that could arise in these challenging problems and help to decide with confidence on which tool to select in order to achieve accurate estimation of the failure probabilities within feasible times with their available computational capabilities.

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“…More specifically, Christou et al (2018), Vlachos et al (2018), and Suksuwan and Spence (2018) address issues related to seismic and wind hazards. Zhang and Taflanidis (2018), Moustapha et al (2018), and Sundar and Shields (2019) discuss and compare approaches for surrogate model development-most notably Kriging-and support-vector-regression-based techniques. Naess and Bo (2018), Zhang and Taflanidis (2018), and Sundar and Shields (2019) further discuss issues related to sampling for Monte Carlo simulations or surrogate model development, while Christou et al (2018) employs an optimal set of random field samples for hazard modeling.…”

mentioning

confidence: 99%

“…A surrogate modeling technique of particular interest is the Kriging (or Gaussian process) model that is studied extensively in this special collection. The paper by Moustapha et al (2018) compares the Kriging model with support vector regression to assess their relative efficiency. In this comparison, the authors specifically uncover the importance of introducing anisotropy in the model hyperparameters through a carefully automated efficient global search algorithm.…”

mentioning

confidence: 99%

Advances in Simulation-Based Uncertainty Quantification and Reliability Analysis

Shields

Sudret

2019

ASCE-ASME J. Risk Uncertainty Eng. Syst., Part A: Civ. Eng.

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The special collection on Advances in Simulation-Based Uncertainty Quantification and Reliability Analysis is available in the ASCE Library (https://ascelibrary.org/page/ajrua6/simulation _based_uncertainty_quantification_reliability_analysis). Simulations are increasingly being used in lieu of or to supplement physical testing in several major industries from civil structural analysis and design to the automotive, aircraft, and naval industries. Two critical aspects of simulation-based analysis and design are the rigorous quantification of uncertainty and the ability to rapidly and accurately assess reliability. Monte Carlo simulation is the most robust simulation-based approach for such problems and serves as a benchmark against which new methods can be compared. The well-known problem with Monte Carlo methods, especially for reliability assessment, is their large computational expense imposed by the requirement of running a very large number of simulations. In recent years, rapid advances that improve on classical Monte Carlo simulation, coupled with improvements in computational resources, have begun to usher in a new era of simulation-based uncertainty analysis such that modern challenges, e.g., uncertainty quantification (UQ) for very large (e.g., highdimensional, computationally intensive) and complex (e.g., strongly nonlinear, multicomponent, multiscale, multiphysics) systems and inverse problems, are becoming increasingly tractable with a reasonable number of simulations. Examples of new methods include Markov chain Monte Carlo (MCMC) approaches such as subset simulations, sparse-grid stochastic collocation methods, Bayesian nested sampling, variance reduction techniques (i.e., Latin hypercube, importance sampling), and new adaptive Monte Carlo and quasi-Monte Carlo methods. This special collection aims at exploring the latest methodological developments in simulation-based uncertainty quantification and reliability analysis. The genesis of this special collection was a series of minisymposia on the topic organized by the coeditors and colleagues held at the 2016 Probabilistic Mechanics and Reliability Conference, the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, and the 12th International Conference on Structural Safety and Reliability. These minisymposia saw a total of 39 speakers addressing some of the most pressing issues in computational uncertainty quantification and reliability analysis. Among these presenters,

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Comparative Study of Kriging and Support Vector Regression for Structural Engineering Applications

Cited by 47 publications

References 48 publications

A Gaussian process latent force model for joint input-state estimation in linear structural systems

A Gaussian process latent force model for joint input-state estimation in linear structural systems

On the Robust Estimation of Small Failure Probabilities for Strong Nonlinear Models

Advances in Simulation-Based Uncertainty Quantification and Reliability Analysis

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