PaperlayerView exact revision on arXiv

Source-linked AI summary

Stripe-Based Fragility Analysis of Concrete Bridge Classes Using Machine Learning Techniques

Sujith Mangalathu, Jong-Su Jeon

arXiv:1807.09761v1cs.CEcs.LGstat.ML

TL;DR

Single-parameter bridge fragility curves can require costly re-simulation after input updates and do not show the relative importance of uncertain variables. This paper combines stripe analysis and Random Forests to generate bridge-specific fragility without a demand-model assumption. It reports that the traditional lognormal demand assumption leads to unrealistic fragility curves.

  • Problem

    Single-parameter fragility curves can require expensive re-simulation after input updates and cannot identify the relative importance of uncertain input variables.

    Source: INTRODUCTION · p. 3

  • Method

    The paper uses Random Forests with stripe analysis to establish a predictive equation for bridge-specific fragility.

    Source: CONCLUSIONS · p. 16

  • Results

    The traditional lognormal assumption on the seismic demand model leads to unrealistic fragility curves.

    Source: CONCLUSIONS · p. 17

  • Takeaways & Limitations

    The approach generates bridge-specific fragility without imposing a demand-model assumption.

    Source: CONCLUSIONS · p. 16

    The methodology is demonstrated for selected bridge classes.

    Source: CONCLUSIONS · p. 17

Abstract

from arXiv · show

A framework for the generation of bridge-specific fragility utilizing the capabilities of machine learning and stripe-based approach is presented in this paper. The proposed methodology using random forests helps to generate or update fragility curves for a new set of input parameters with less computational effort and expensive re-simulation. The methodology does not place any assumptions on the demand model of various components and helps to identify the relative importance of each uncertain variable in their seismic demand model. The methodology is demonstrated through the case studies of multi-span concrete bridges in California. Geometric, material and structural uncertainties are accounted for in the generation of bridge models and fragility curves. It is also noted that the traditional lognormality assumption on the demand model leads to unrealistic fragility estimates. Fragility results obtained the proposed methodology curves can be deployed in risk assessment platform such as HAZUS for regional loss estimation.

INTRODUCTION

The paper addresses limits of single-parameter bridge fragility curves and presents a multi-parameter, random-forest methodology built on stripe analysis. It is demonstrated for three- and four-span California bridges, accounting for geometric, structural, and material uncertainties.

INTRODUCTION

  • Single-parameter fragility curves can require expensive re-simulation after input updates and cannot identify each uncertain variable’s relative importance.They also require grouping bridges with statistically similar performance before fragility analysis.Source: INTRODUCTION · p. 3
  • The paper questions lognormal demand assumptions, citing prior work that they can introduce significant error into fragility curves and loss estimates.At high intensity measures, nonlinear component behavior may also produce demand-model statistical errors when intensity is the only conditioned variable.Source: INTRODUCTION · p. 3
  • The proposed methodology combines stripe analysis with Random Forests to generate multi-parameter fragility curves without assuming a demand-model form or dispersion.The paper identifies this as an unexplored application of Random Forests with the stripe approach.Source: INTRODUCTION · pp. 3–4
  • The study demonstrates the methodology on three- and four-span California bridges and accounts for geometric, structural, and material uncertainties.The selected bridge types were reported to occupy more than 40% of the California bridge inventory, while few studies had explored their vulnerability.Source: INTRODUCTION · p. 4
  • The study compares RF fragility results with existing stripe methodology and examines normality assumptions and the relative importance of uncertain inputs.Source: INTRODUCTION · p. 4

Random Forest

Random Forests combine predictions from multiple decision trees. In this paper’s description, bootstrap sampling and randomized feature selection shape the trees, while aggregated predictions provide the output.

Random Forest

  • Random Forest is an ensemble of tree structures whose predictions are aggregated to produce an output.The paper describes the output as the average prediction across the trees.Source: Random Forest · p. 5
  • At each node, Random Forest selects a random subset of features for splitting, extending bagging’s use of independently trained trees on bootstrap samples.The trees’ mean output is used for prediction.Source: Random Forest · p. 5
  • The method estimates error by aggregating predictions for out-of-bag data and calculating an error rate.Out-of-bag data are observations absent from each tree’s bootstrap sample.Source: Random Forest · p. 6

Numerical Modeling of Selected Bridges, Uncertainties, and Ground Motions

The study builds bridge models for selected California bridge types and accounts for uncertainties in their inputs. It pairs sampled models with ground motions for nonlinear time-history analysis.

Numerical Modeling of Selected Bridges, Uncertainties, and Ground Motions

  • The study selects three- and four-span California bridges and accounts for geometry, material, and system uncertainties in model inputs.Input-variable choices draw on bridge-component modeling and prior sensitivity-study insights.Source: Numerical Modeling of Selected… · pp. 6–7
  • Bridge component models include nonlinear column elements and representations of abutments, bearings, foundations, and pounding.Columns use displacement-based beam-column elements with fiber-defined cross-sections; bearings use an elasto-plastic model and pounding an inelastic compression element with a gap.Source: Numerical Modeling of Selected… · pp. 6–7
  • Latin Hypercube Sampling generates statistically varied bridge models across the input-parameter ranges, covering the probability space more effectively than naïve Monte Carlo sampling.Source: Numerical Modeling of Selected… · p. 8
  • The generated bridge models are randomly paired with ground motions for nonlinear time-history analysis, with the two orthogonal motion components randomly assigned to bridge directions.The study adopts spectral acceleration at 1 sec (Sa–1.0) as the intensity measure.Source: Numerical Modeling of Selected… · p. 8

Existing Stripe-Based Fragility Methodology

The existing stripe-based method scales ground motions to selected intensity levels, fits lognormal distributions to component demands, and combines demand with capacity to estimate failure probabilities. The resulting fragility curve depends on a normality assumption at each intensity level.

Existing Stripe-Based Fragility Methodology

Proposed Stripe-Based Fragility Methodology Using Random Forest

The proposed random-forest stripe method generates or updates fragility curves without assuming a demand-model form, and identifies the relative importance of uncertain variables. It uses sampled bridge models and predicted demands to estimate failure probabilities, while assuming lognormal capacity models.

Proposed Stripe-Based Fragility Methodology Using Random Forest

  • The methodology can update fragility curves for changed input parameters without expensive re-simulation and identify variable importance at each IM.Its identification of influential parameters can help bridge owners prioritize updates to their input-parameter database.Source: Proposed Stripe-Based Fragility… · p. 10
  • The method makes no assumptions about the demand model because its random-forest-based demand model is non-parametric.The study assumes lognormal capacity models; developing bridge-attribute-related capacity models is beyond its scope because extensive experimental data are needed.Source: Proposed Stripe-Based Fragility… · pp. 10, 12
  • The workflow samples bridge models with Latin Hypercube sampling, scales ground motions to target IMs, and trains random forests to predict component demand.The predictive model uses IM, Tm, and modeling parameters as inputs; logarithms of input and output data are used to reduce nonlinearity.Source: Proposed Stripe-Based Fragility… · p. 11
  • For each component, the method compares sampled demands with capacity values to estimate failure probability and repeats this across IMs to construct fragility curves.The study generates one million demand estimates per component; bridge-specific curves account for material nonlinearity and Tm.Source: Proposed Stripe-Based Fragility… · p. 11

Performance Evaluation of Various Machine Learning Methods

Random forests show the best predictive capability among the evaluated regression methods across IM levels, and the traditional lognormal demand assumption is rejected for tested EDPs. Compared with the existing stripe method, the proposed method produces less dispersed fragility curves while retaining similar median values.

Performance Evaluation of Various Machine Learning Methods

  • Random forests have the best predictive capability, with higher R2 and lower MSE than the compared methods across IM levels and components.The comparison evaluates lasso regression, elastic net, SVM, and random forests; the reported examples are column curvature ductility and bearing displacement.Source: Performance Evaluation of Various… · p. 12

Checking Normality Assumption in Traditional Stripe Analysis

  • P-values close to zero for μϕ and δb indicate those demands do not follow a lognormal distribution, and the assumption is not valid for all studied EDPs.The Kolmogorov–Smirnov test rejects lognormality when its p-value is below 0.05.Source: Checking Normality Assumption in… · p. 13

Comparison of Traditional and Proposed Methodology

  • The proposed method has less dispersion and a stiffer slope than the existing stripe method across components and limit states, with no substantial statistical difference in median fragilities.The comparison covers selected combined three- and four-span bridge classes.Source: Comparison of Traditional and Proposed… · p. 13

Relative Importance of Uncertain Parameters at Each IM

Random-forest importance analysis identifies which uncertain parameters most influence seismic demand, with the influential variables depending on the EDP and IM. The findings also indicate that neglecting uncertainty in influential parameters can yield unreliable or unrealistic fragility curves.

Relative Importance of Uncertain Parameters at Each IM

  • Span length, longitudinal reinforcement ratio, column height, approach-span-to-main-span ratio, and deck width significantly influence demand across EDPs.The analysis interprets variable importance for the demand model under the uncertainties reported in Table 1.Source: Relative Importance of Uncertain… · p. 14
  • Variable influence depends on the EDP: abutment pile stiffness matters for abutment responses in passive, active, and transverse directions, but not for column curvature ductility.Column curvature ductility is also significantly affected by column diameter, column height, and longitudinal reinforcement ratio across IMs.Source: Relative Importance of Uncertain… · pp. 14–15
  • Relative importance changes with IM; span length has higher importance at Sa-1.0 = 0.6g than at the comparison intensity stated in the analysis.The provided passage does not preserve the comparison intensity value.Source: Relative Importance of Uncertain… · p. 14
  • Neglecting uncertainty in influential parameters such as span length, longitudinal reinforcement ratio, column height, approach-span ratio, and deck width leads to unreliable fragility curves.Importance estimates can quantify the associated error from inadequate uncertainty evaluation; errors in span-length uncertainty can produce unrealistic curves, whereas errors in mf uncertainty may have minimal impact.Source: Relative Importance of Uncertain… · pp. 14–15
  • The stated mechanisms link span length and approach-span ratio to increased deck mass and flexibility, and link column variables to column strength and stiffness.Abutment response is tied to backfill soil type, abutment height, and pile stiffness through the abutment force-displacement relation.Source: Relative Importance of Uncertain… · p. 15

Component Vulnerability of Selected Bridge Configurations

The study generates fragility curves for combined three- and four-span bridge configurations and reports little statistical difference between their fragilities. Fitted curves closely match the actual failure-probability points, and the resulting median and dispersion values are intended for regional risk and loss estimation.

Component Vulnerability of Selected Bridge Configurations

  • The study notes little statistical difference between the fragilities of three-span and four-span bridges, and reports that this observation is consistent with previous work grouping bridge classes by seismic demand.The cited prior work is Mangalathu 2017 and Mangalathu et al. 2017.Source: Component Vulnerability of Selected… · p. 15
  • Fitted and actual fragility curves are almost identical across EDPs and limit states in the reported comparison.The comparison covers moderate (LS2) and complete (LS3) damage states; median and dispersion values are provided for components across four limit states.Source: Component Vulnerability of Selected… · p. 16
  • The reported fragility values for three- and four-span bridges can be used for regional risk and loss estimation.The developed random-forest-based curves are represented as lognormal cumulative distribution functions with median λ and dispersion β for practical use in platforms such as HAZUS.Source: Component Vulnerability of Selected… · pp. 15–16

CONCLUSIONS

The paper presents a stripe-based, random-forest framework for generating bridge-specific fragility curves without assuming a seismic demand model. It demonstrates the approach for California bridges and identifies influential uncertain variables, with potential use in regional risk assessment.

CONCLUSIONS

  • The proposed framework combines stripe analysis and machine learning to generate bridge-specific fragility curves without assumptions on seismic demand.The paper describes the resulting fragilities as more reliable for regional bridge risk assessment.Source: CONCLUSIONS · p. 16
  • Numerical bridge models incorporating material and geometric uncertainties are created in OpenSees and paired with scaled ground motions for nonlinear time-history demand estimation.The demonstrated study also accounts for structural uncertainties.Source: CONCLUSIONS · p. 16
  • Random Forests connect uncertain input parameters to component demands, which are compared with capacities to generate fragility curves for new inputs without expensive simulation.The considered demands include column curvature ductility, abutment displacement, superstructure unseating displacement, and elastomeric bearing displacement.Source: CONCLUSIONS · pp. 16–17
  • The traditional lognormal assumption on seismic demand produces unrealistic fragility curves.The paper contrasts this assumption with its methodology, which makes no assumption on seismic demand.Source: CONCLUSIONS · pp. 16–17
  • Span length, approach span-to-main span ratio, longitudinal reinforcement ratio, deck width, and column height significantly influence seismic demand and fragilities across bridge components.The methodology identifies these variables as influential across all components.Source: CONCLUSIONS · p. 17
  • The methodology generates fragility curves for three- and four-span California bridges, with suggested use in regional risk platforms such as HAZUS for seismic loss estimation.Although demonstrated for selected bridge classes, the paper states that the methodology is applicable to other structural systems.Source: CONCLUSIONS · p. 17
Loading 1807.09761v1…