Previous section defines the most appropriate surrogate models for bridge deck
unseating classification. The results from the FSI Model methodology were
implemented to develop these surrogate models. However, the efficiency of fragility
analysis can be further improved by using more simplified structural analysis
models, as long as it is capable of capturing the failure mode of interest. Fluid-
structure interaction models such as the one presented in Section 4.2 have the
advantage of accurate estimation of the bridge behavior and providing insight on
the response of the bridge but they are computationally intense as noted in Section
6.3.
Therefore, this section constructs reliability surrogate models on the output
of the MCS Static and Dynamic Models, and compares them with the reliability
surrogate model constructed from the FSI Model. The same case study bridge
model with the same experimental design and approach presented in Section 6.3 is
utilized here; however, the output data used to derive the surrogate model is based
and the Static Model. The full set of random variables for this simulation is
presented in Appendix V.
Two random forests are trained over the results of the MCS Static Model
output and Dynamic Model output, respectively. The resultant random forests are
designated as S-RF and D-RF, respectively. Since all random forests algorithms are
already constructed based on the training data, predicted failure probabilities can
be directly estimated for any Hmax and Zc. A sample size of 10,000 points over the
hazard intensity measures is generated and used to identify the misclassification
error for the other models versus FSI. The trained random forests are compared
with the FSI-RF in Figure 7-3. The S-RF and D-RF are in agreement with the
FSI-RF. The misclassification errors for these two random forests with respect to
FSI-RF are 0.19 and 0.13, respectively. Since the random forests surrogate model
has high accuracy (the surrogate model error is around 0.01), the misclassification
error is due to the reduction in the structural analysis and load modeling accuracy
from the FSI Model to the Dynamic and Static Models. Confusion matrices are
shown in Table 7-3. As it can be concluded, the results of the MCS Static and
Dynamic Models are conservative; (i.e., more false negatives are reported than false
susceptible bridges structures under hurricane events. The F1-measures for the S-
RF and D-RF models compared to FSI-RF are 0.65 and 0.75 respectively. This
result shows that the higher accuracy is achieved by using more advanced models.
However, fast screening of vulnerable coastal bridges, especially for real time
application, is more practical with the MCS Static and Dynamic Models.
Figure 7-3. Comparison of two random forests models trained over different analysis output data: (a) FSI Model versus Static Model; (b) FSI Model versus Dynamic
Model.
Table 7-3. Confusion matrices for three random forests models trained over FSI, Static and Dynamic Models output.
A ct u a l cl a ss (F S I) Predicted class (Static) Predicted class (Dynamic)
Survived Failed Survived Failed
Survived 6484 1599 7119 964
7.4. Summary
This chapter and Chapter 6 present the core contribution of this research for the
development of fragility models for coastal bridges subjected to hurricane induced
wave and surge loads. The results of the structural analysis models presented in
Chapter 5 reveal that deck unseating is a brittle failure mode. Therefore, the
output becomes a categorical data; i.e., failed (unseated) or survived (seated). A
continuous model over the entire range of hazard intensity measures is required to
be constructed on this categorical data that can provide failure probabilities for
any realization of hazard parameter (that may not be simulated). Surrogate models
that relate continuous input to categorical output are required. Therefore
traditional response surface models are not appropriate. Three statistical learning
methods —logistic regression, support vector machines, and random forests— are
applied to the result of the analysis of bridge deck unseating. These methods are
nonlinear classifiers that can provide high accuracy classification for binary data.
Logistic regression, support vector machines with the Gaussian radial basis
function kernel, and random forests provide a high quality approximation of the
bridge deck unseating failure mode. Nonetheless, the performance of the random
Random forests surrogate models are trained over the results of Static, Dynamic,
and FSI Models and compared to each other, where the output of FSI Model is
considered as the most accurate and the basis for comparison. The result of the
Dynamic Model is in good agreement with the FSI Model, and therefore, can be
used for a more computationally efficient reliability assessment. The error increases
as the modeling accuracy decreases; i.e., Static Model has higher error than
Dynamic Model. However, the Static Model can provide an effective means to
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Chapter 8
Retrofit Measures for Coastal Bridges
and Definition of New Capacity Limit
State Functions
This chapter introduces potential retrofit measures for coastal bridges to prevent
the deck unseating failure mode. Providing strong connections between the bridge
super- and substructure is one of the recommended methods for retrofitting coastal
bridges (Padgett et al. 2008; Padgett et al. 2009; Sawyer 2008). Other retrofit
measures, such as shear keys and restrainer cables that traditionally have been
used for seismic hazard mitigation of highway bridges, can also be used for coastal
bridges to prevent deck unseating. All of these measures can potentially transfer
state is not simply a deck displacement value, as considered in the fragility analysis
in prior chapters of this dissertation. The transferred forces may introduce damages
to the substructure which have not been explored in past research. This chapter
introduces the potential retrofit measures to prevent deck unseating failure mode.
Also, new capacity limit state functions for retrofitted bridges are defined. Chapter
9 will apply the approach to derive capacity limit state functions to evaluate the
viability of the prospective retrofits to improve the reliability of coastal bridges in
the Houston/Galveston area inventory.