[Paper Review] Efficient Seismic fragility curve estimation by Active Learning on Support Vector Machines

Rémi Sainct, Cyril Feau+2 more|arXiv (Cornell University)|Sep 25, 2018

Structural Health Monitoring Techniques20 references4 citations

TL;DR

This paper proposes an active learning framework using Support Vector Machines (SVMs) to efficiently estimate non-parametric seismic fragility curves with minimal structural analysis computations. By treating structural response as a binary classification problem based on failure thresholds and using SVM scores as probabilistic intensity measures, the method achieves high accuracy with only 100–1,000 simulations, outperforming traditional PGA-based fragility curves and parametric models in steepness and precision.

ABSTRACT

Fragility curves which express the failure probability of a structure, or critical components, as function of a loading intensity measure are nowadays widely used (i) in Seismic Probabilistic Risk Assessment studies, (ii) to evaluate impact of construction details on the structural performance of installations under seismic excitations or under other loading sources such as wind. To avoid the use of parametric models such as lognormal model to estimate fragility curves from a reduced number of numerical calculations, a methodology based on Support Vector Machines coupled with an active learning algorithm is proposed in this paper. In practice, input excitation is reduced to some relevant parameters and, given these parameters, SVMs are used for a binary classification of the structural responses relative to a limit threshold of exceedance. Since the output is not only binary, this is a score, a probabilistic interpretation of the output is exploited to estimate very efficiently fragility curves as score functions or as functions of classical seismic intensity measures.

Motivation & Objective

• To develop a non-parametric, computationally efficient method for estimating seismic fragility curves without relying on parametric assumptions like lognormal distribution.
• To reduce the number of costly nonlinear time-history analyses required in seismic probabilistic risk assessment (SPRA).
• To identify the optimal seismic intensity measure indicator by using SVM scores instead of conventional parameters like PGA.
• To address the limitations of parametric models in representing complex structural behavior under seismic excitation.
• To integrate active learning with SVMs to intelligently select the most informative simulations, minimizing computational burden.

Proposed method

• Reduce seismic input to relevant parameters (e.g., PGA, V, L, ω₀) using a Box-Cox transformation to improve SVM performance.
• Use a binary classification SVM to determine whether a structure exceeds a failure threshold for each seismic input sample.
• Employ active learning to iteratively select the most uncertain or informative simulations for labeling, minimizing the number of required analyses.
• Utilize the SVM decision function output (a 'score') as a probabilistic intensity measure for fragility curve estimation.
• Interpret the SVM score as a failure probability estimate, enabling construction of fragility curves as score functions or against classical intensity measures.
• Combine linear and RBF kernel SVMs in a hybrid strategy: use linear for high-confidence predictions and RBF for uncertain regions to improve robustness.

Experimental results

Research questions

• RQ1 Can active learning with SVMs significantly reduce the number of structural analyses required to estimate seismic fragility curves?
• RQ2 Is the SVM score a more accurate and steeper intensity measure indicator than traditional parameters like PGA?
• RQ3 How does the performance of linear versus RBF kernel SVMs compare in terms of fragility curve accuracy and computational cost?
• RQ4 Can a hybrid SVM approach combining linear and RBF kernels improve robustness without sacrificing accuracy?
• RQ5 To what extent does data preprocessing (e.g., Box-Cox transformation) enhance the performance of linear SVMs in fragility curve estimation?

Key findings

• Using only 100 simulations with a linear SVM and Box-Cox preprocessing, the method achieved a fragility curve with a 1.8% L₂ error relative to a reference Monte Carlo curve.
• The score-based fragility curve was steeper and more accurate than the PGA-based curve, indicating better discrimination of failure potential.
• The L-based fragility curve performed comparably to the PGA-based curve in the tested setting.
• The RBF kernel required 1,000 simulations to achieve a PRBP of 0.85, but produced a catastrophic 20% L₂ error when used alone, indicating instability for fragility curve construction.
• The hybrid approach using linear SVM for high-confidence regions and RBF for uncertain regions achieved a 2.3% L₂ error, significantly better than pure RBF and close to the best-performing linear method.
• The SVM score was shown to be a valid and effective intensity measure indicator, with the potential to replace or outperform traditional seismic parameters.