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17th World Conference on Earthquake Engineering, 17WCEE
Sendai, Japan - September 13th to 18th 2020
Paper N° C003486
Registration Code: S-A02822
Surrogate Modeling for the Seismic Response Estimation of
Residential Wood Frame Structures
J. Zou(1), D. P. Welch(2), A. Zsarnoczay(3), A. Taflanidis(4), G. G. Deierlein(5)
(1) Graduate Student, Dept. of Civil & Environmental Engineering, Stanford University, zouj@stanford.edu
(2) Postdoctoral Researcher, Dept. of Civil & Environmental Engineering, Stanford University, dpwelch@stanford.edu
(3) Postdoctoral Researcher, Dept. of Civil & Environmental Engineering, Stanford University, adamzs@stanford.edu
(4) Professor, Dept. of Civil & Environmental Engineering and Earth Sciences, University of Notre Dame, a.taflanidis@nd.edu
(5) Professor, Dept. of Civil & Environmental Engineering, Stanford University, ggd@stanford.edu
Abstract
Existing residential wood frame structures account for a significant portion of the seismic vulnerability of a geographic
region, as earthquake-induced damages can lead to loss of housing and broad disruption to communities. In probabilistic
seismic performance assessment, the standard method of using nonlinear response history analysis to estimate the seismic
response of a structure presents a high computational cost which limits the scale of regional-level earthquake simulations.
This study presents a surrogate model-based solution for the efficient seismic response estimation of residential wood
frame structures for applications in regional seismic performance assessment. Kriging is adopted as the framework for
developing an approximate functional relationship between input parameters representing properties of the structural
model and ground motion excitation and corresponding output parameters providing measures of collapse fragility,
median seismic response, and prediction variance. An initial set of surrogate models are formulated for a case study
building to evaluate the accuracy of the kriging metamodel prediction and illustrate the influence of structural properties
on the seismic vulnerability of residential wood frame structures.
Keywords: seismic performance assessment; residential wood buildings; surrogate modeling; kriging
1. Introduction
Performance-based earthquake engineering (PBEE) is a method of assessing a building's expected ability to
meet service needs under risks to extreme loads from earthquakes [1]. This particular application of
probabilistic risk analysis, also referred to as seismic performance assessment, has generally focused on
evaluating the likely damages to an individual building under varying levels of seismic hazard. However, by
increasing the scope to evaluate a population of buildings, seismic performance assessments can quantify social
and economic risks across a city or municipality. This regional-level perspective is valuable in guiding
decisions regarding natural disaster mitigation policies, catastrophe insurance, and real estate development.
From past earthquake events, there is evidence that one- to two-story residential wood frame structures
contribute significantly to regional seismic performance assessments of earthquake-induced damages and
losses. For instance, in the 1994 Northridge M6.7 earthquake, residential wood frame structures contributed to
more than half of the 40 billion dollars in property damage caused by the earthquake [2]. Nearly all of the
48,000 housing units which were rendered uninhabitable after the earthquake were wood frame structures [3].
After the 2014 South Napa M6.0 earthquake, survey results demonstrated that the predominant housing type
experiencing damage was wood frame structures; 1 in 3 of such structures built before 1950 were red tagged
or yellow tagged during inspection, indicating that its occupancy poses a potential safety hazard. 48% of
homeowners of wood frame units reported spending over a week on clean-up and repairs, and 20% reported
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17th World Conference on Earthquake Engineering, 17WCEE
Sendai, Japan - September 13th to 18th 2020
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that important repairs had not been completed seven months later [4]. The disruption to society caused by
housing losses demonstrates the importance of understanding and reducing the seismic vulnerability of wood
frame residential units, in order to increase the overall resilience of a community to earthquake disasters.
Large-scale seismic performance assessments of regions pose the challenge of requiring significant
computational resources. In a seismic performance assessment by the FEMA P-58 methodology [1], seismic
risk is quantified by a general procedure: first, ground motions corresponding to multiple earthquake intensities
are selected to provide a comprehensive characterization of seismic hazard at a given site [5]. Then, seismic
response is estimated by nonlinear response history analysis of a numerical (finite element) model representing
the building structure, a routine which is iterated for multiple ground motions at varying intensity levels.
Finally, fragility and consequence functions relate the resultant estimates for peak seismic response, such as
lateral drift and acceleration, with expected damage to the structure and associated losses. The intermediate
step of nonlinear response history analysis is the most computationally intensive part of the seismic
performance assessment procedure and a major limitation to the number of iterations of the routine that is
feasible within the time and resources allotted to a project. In order to address this challenge, past studies [6,
7] have constrained the number of structures considered for earthquake simulation, by categorizing buildings
in an urban system into a smaller suite of building classes, or “archetypes”. Whereas this “high-fidelity”
approach provides high accuracy estimates of seismic response using detailed nonlinear structural models of
each archetype, the diverse range of possible construction eras, material types, and geometric configurations
of existent residential wood frame structures in North American regions is not adequately characterized by
only a few chosen archetypes. Other studies [8] have examined the use of simplified lumped-mass and lumped-
stiffness structural models in order to reduce model complexity and the computational demand of the nonlinear
response history analysis. However, this “high-efficiency” approach lacks the accuracy and spatial resolution
necessary to capture geometric nonlinear effects, which often governs the true dynamic behavior or failure
modes of light-frame wood structures.
The present study proposes the development of a surrogate model to provide an efficient computational
framework for structural response estimation which maintains the fidelity of the high-resolution structural
model. The function of the surrogate model is to provide an approximation of the complex functional
relationship between input parameters of material and geometric properties characterizing the building
archetype and the output parameters of peak response metrics describing the seismic behavior of the structure.
The proposed approach uses kriging metamodeling as the technique for the surrogate model formulation, in
which hyperparameters of the surrogate model are optimally tuned according to a sufficiently large training
database of simulated response data [9]. Kriging is a regression method which not only predicts an output
value corresponding to a set of inputs, but also estimates the confidence of the prediction by accounting for
the probability of observance for each input-output pair; thus, for intermediate values between the training
data, kriging offers the best linear unbiased estimate compared to other interpolation methods [10]. With these
capabilities, the surrogate model provides several advantages over conventional methods of seismic response
estimation:
1) Seismic response estimation can be performed using the surrogate model in lieu of nonlinear response
history analysis, thereby significantly reducing the computational cost of the estimation.
2) Using confidence information, the accuracy of the surrogate model can be assessed during its
development, such that the application of adaptive training techniques allows the surrogate model to
achieve high accuracy estimates [8].
3) The low-cost, high-accuracy performance of the surrogate model improves the practicality of regional-
level seismic performance assessments by significantly reducing the computational demand of
simulations for a large number of buildings at multiple earthquake intensity levels.
4) The surrogate model provides the ability to efficiently quantify the effect of variability in structural
properties on the uncertainty in peak seismic response values and estimated structural damage.
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Using this approach, a case study building of a wood frame structure illustrates the capabilities of
surrogate modeling for the seismic response estimation step of the FEMA P-58 seismic performance
assessment methodology [1]. The paper is organized as follows: Section 2 demonstrates the approach for
translating structural properties and site information of a case study wood frame structure into sample
simulations for the training database. Section 3 presents the kriging framework for formulating the surrogate
model. Section 4 assesses the performance of the surrogate model in comparison to high-fidelity simulation
data. Finally, Section 5 discusses challenges in the development and implementation of the surrogate model to
overcome in future research.
2. Structural Model Development
2.1 Case Study Structure and Site
To evaluate a variety of possible building ages, material types, and geometric configurations, the case study
considers multiple archetypes of a residential wood frame structure, each described by varying the material
properties of a chosen baseline archetype. The building considered for the baseline archetype is a 1-story single
family dwelling with a uniform height unreinforced cripple wall level. The layout of the building is modeled
after the CUREE Small House [7], selected to represent a typical single-family residential unit. The building
is characterized by a 40’ by 30’ footprint, 2-foot tall cripple wall with a stucco finish, and 9-foot tall
superstructure. Consistent with the majority of older residential wood frame structures, the exterior and interior
finishes of the walls of the cripple wall and superstructure provide the primary lateral force resisting structural
system for sustaining horizontal loading from earthquake ground motions.
The case study seismic performance assessment is for a site in San Francisco, California, situated
between the Hayward Fault and San Andreas Fault. Ten earthquake intensity levels are chosen to characterize
seismic hazards ranging from a 15-year return period to a 2500-year return period. 45 pairs of orthogonal
horizontal ground motions with target Vs,30 = 270 m/s are selected to match a conditional spectrum (mean and
variance) [5] using a conditioning period of 0.25 seconds, using RotD50 spectral acceleration as the earthquake
intensity measure. Site hazard and ground motions are used directly from a study from the ongoing
collaboration between the Pacific Earthquake Engineering Research Center (PEER) and California Earthquake
Authority (CEA) [7].
2.2 Structural Analysis Model
The baseline archetype is represented as a 3D finite element model in OpenSees [11]. The floor and roof are
modeled as rigid diaphragms. The cripple walls and exterior superstructure walls are modeled as single lumped
plasticity elements located at the midpoint of each face of the structure, assigned with the aggregate length of
the corresponding wall excluding lengths of window or door openings. Interior superstructure walls are
similarly modeled with two lumped plasticity elements representing aggregate wall lengths (Fig. 1a). Mass
and gravity loads contributed by the diaphragms and walls are assigned to an array of leaning columns modeled
with corotational truss elements. Inherent damping is applied as 2.5% tangent stiffness-proportional Rayleigh
damping to the wall elements and diaphragm nodes at the first and third elastic modal periods.
A primary high-fidelity feature of the model is the representation of nonlinear hysteresis of the wall
materials using a four-point backbone curve, describing the monotonic force-displacement relationship of the
material. Superstructure materials include combined stucco and gypsum wallboard for exterior walls and
interior gypsum wallboard for partitions. From interpretation of cyclic loading experiments for stucco cripple
wall, conducted as a part of the PEER-CEA Project [7] and CUREE Woodframe Project [12], separate
backbone curves corresponding to three grades of existing cripple wall material quality – ‘poor’, ‘average’,
and ‘good’ – are developed by calibrating material parameters characterizing the four points of the backbone
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Sendai, Japan - September 13th to 18th 2020
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curves (Fig. 1b). The backbone parameters for the superstructure materials reflect the best estimates of material
properties in line with the discussion provided in Chapter 4 of FEMA P-1100-3 [13].
The structural model is constructed using a class of functions in an object-oriented framework which
utilizes OpenSeesPy [14], a Python interpreter for OpenSees. The framework produces a high-fidelity finite
element model based on a set of input parameters, defined by attributes for the total floor plan area, the plan
aspect ratio, the material quality of the cripple wall, number of stories, story heights, floor weights, wall
materials, and wall lengths. This parametric approach to finite element modeling facilitates the rapid
construction of structural models for each archetype, used to populate the training database for the surrogate
model. For general applications, the class is publicly accessible as a model generation tool for developing high-
fidelity structural models of residential wood frame structures in OpenSeesPy, compatible with Python
workflows for seismic response estimation (github.com/joannajzou).
For developing an initial proof-of-concept surrogate model, only a subset of possible structural model
parameters are selected as variables for differentiating archetypes: the quality of the cripple wall material (),
the floor plan area (), and the floor plan aspect ratio (). These three variables are chosen for their high
influence on the stiffness and strength properties of the cripple wall level and the resulting variability in the
deformation capacity and dynamic response of the structure. To describe the material quality of the cripple
wall, the discrete grade classifications from experiments are translated into a continuous quality score , where
a score of 0.0 corresponds to material backbone parameters of the ‘poor’ rating and a score of 1.0 corresponds
to material backbone parameters of the ‘good’ rating. The floor plan dimensions (length and width) are
computed from the given values of and . The aggregate lengths of exterior and interior walls are assumed
to be a fixed proportion of the total length of each dimension. All other model features and weight takeoff
schemes are consistent with that of the baseline archetype.
Fig. 1 – (a) Dimensions of baseline archetype. (b) Four-point backbone curve of 2’-0” stucco cripple wall
elements for three ratings of material quality.
Seismic response estimation for each archetype is performed to generate the training database of
simulations, referred to as “sample experiments”. The NHERI-SimCenter EE-UQ workflow on the
DesignSafe-CI platform [15] provided cloud-based high performance computing resources for performing the
nonlinear response history analysis procedure. The outputs of each simulation are peak interstory drifts and
peak floor accelerations at the cripple wall level and roof level of the structure, with separate peak values
recorded for two orthogonal horizontal directions.
(a)
(b)
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3. Surrogate Model Development
3.1 Kriging Formulation
The kriging metamodel approximates complex functional relationships between a set of inputs
and a set of corresponding outputs for number of
sample experiments, where each sample experiment receives number of input parameters and returns
number of response output values. For the th dimension of the output values ( ), the true response
is estimated from the kriging prediction and the corresponding prediction error :
(1)
The mean prediction is determined by the combination of two components: global behavior of the
functional relationship is captured by a set of basis functions, whereas local behavior about the regression
residuals is estimated by a zero-mean Gaussian process. For global regression, the basis vector
is comprised of basis functions, in which , may be taken as a constant (0th
order approximation) or a higher order polynomial for greater prediction accuracy. For the present application,
it is sufficient to take to be a full quadratic basis [9] of the form:
(2)
For local fitting, the Gaussian process has a mean of zero and covariance matrix , of
which the latter depends on the process variance and correlation matrix . Each element
of the correlation matrix defines the interdependency between a pair of samples
and as a function of the distance between the samples. This correlation function may take any form which
produces a positive semi-definite correlation matrix in order to be valid, and it may be chosen based on
the nature of the complex function being approximated [16]. In this study, a generalized exponential correlation
function is implemented, leading to a covariance function with the elements :
(4)
The hyperparameters of the covariance function control the accuracy of the kriging
metamodel. Using maximum likelihood estimation, in which values of are selected to maximize the
likelihood of observing the training database, the hyperparameters are optimally tuned to perform robust
regression of the simulation experiments.
The following procedure is taken to determine the mean output prediction. First, inputs for sample
experiments are generated by Latin hypercube sampling to form the training database. The corresponding
outputs are derived from high-fidelity seismic response simulation. The correlation matrix is
established by computing the correlation between inputs for the sample experiments. The basis matrix is given
as the matrix of basis functions Then, for each new input sample , the
correlation between and the rest of the experiments in the database is defined as the new vector
. Subsequently, the mean kriging prediction for Equation (1) is provided as:
(5)
(3)
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where
(6)
Equation (5) demonstrates that through the correlation matrix, the kriging metamodel couples the effect of
regression and Gaussian process fitting using two terms. The first term governs the global regression using
basis functions and , an -dimensional vector of weighted regression coefficients. The second term governs
local fitting using the optimally tuned correlation functions of the Gaussian process.
Finally, the prediction error in Equation (1) takes a zero-mean Gaussian distribution
, where
is the variance of the kriging prediction of the output. An estimate for
is given by the product of
the process variance (Equation 9) and normalized variance [16]:
(7)
where
(8)
(9)
Using this framework, development of the kriging metamodel has the one-time cost of performing high-fidelity
simulations for generating input-output pairs for the training database. Thereafter, no additional tuning is
required; provided with the kriging regression coefficients and matrices, the only computation for a new input
sample x is for the two terms and to determine the kriging prediction.
3.2 Surrogate Model Approach for Case Study
Kriging metamodeling is implemented for seismic response estimation of the case study building. = 700
sets of inputs are generated to perform sample experiments and create the training database. The input
parameters for each sample experiment are a combination of structural model parameters describing the
building archetype and ground motion parameters describing the excitation force. The input structural model
parameters are the quality of the cripple wall material (), the floor plan area (), and the floor plan aspect
ratio (). To represent the range of typical archetypes for wood frame residential units, the domain of parameter
values is restricted to [0.0, 1.0] for the quality score, [800, 2400] sq. ft. for the plan area, and [0.4, 0.8] for the
plan aspect ratio. The input excitation parameter is the intensity of the earthquake event, expressed in terms of
log of the return period (), sampled from ten discrete values of {15, 25, 50, 75, 100, 150, 250, 500, 1000,
2500} years. Therefore, the input for each sample experiment is a 4-by-1 vector:
.
For each experiment , the high-fidelity structural model is assembled in OpenSees using the framework
detailed in Section 2.2, with the structural model parameters as attributes. Nonlinear response history
analysis is performed with the structural model for = 45 earthquake events, each of which consists of exciting
the model in two orthogonal horizontal directions using a pair of ground motion acceleration time series
selected according to the ground motion parameter
. For each event, the response quantities of peak
interstory drift and peak floor acceleration are taken as the maximum of the absolute value of response
experienced during the ground motion excitation. Structural collapse is assumed to occur in the earthquake
event when the interstory drift at any level of the structure exceeds a threshold of 20%.
Separate surrogate models are established to provide two sets of output predictions corresponding to
each sample. The first kriging provides a prediction of the probability of collapse (), computed as the
ratio of the number of earthquake events experiencing structural collapse to the total number of earthquake
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17th World Conference on Earthquake Engineering, 17WCEE
Sendai, Japan - September 13th to 18th 2020
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events simulated for the given earthquake intensity: When collapse occurs, the nonlinear
response history analysis is subject to numerical instability, with computed drifts of the structural model
approaching infinity. Since we are concerned with measuring the dynamic response of the structure as it
remains standing, to use in the PBEE procedure for assessing damages to the structure, these collapse events
are separated from events in which no collapse occurs in order to preclude these numerical outcomes from
falsely skewing estimates of response quantities. A second kriging provides median and logarithmic standard
deviation predictions for peak interstory drift and peak floor acceleration conditioned on no collapse.
The dynamic response is assumed to follow a lognormal distribution described by the two response statistics.
Response is measured at the center of diaphragm node for each of two levels of the structure (one at the cripple
wall height, the other at the roof level height) in the two horizontal directions, such that the output for each
sample is a 16-by-1 vector:
, for levels , horizontal directions
, and number of sample experiments .
Once the two surrogate models have been trained on the sample experiments, seismic response
estimation may be performed efficiently in the following way. Provided with a new input sample, the first
kriging is implemented to obtain of the structure at the given earthquake intensity. This probability is
used for random sampling of collapse outcomes, to make the binary classification of whether the structure has
collapsed or not. For non-collapse events, the second kriging then makes a prediction of the response output
corresponding to the input sample. The procedure is illustrated in Fig. 2.
Fig. 2 – Conceptual framework for the surrogate model development and implementation.
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4. Results and Discussion
The performance of the surrogate model is evaluated by comparing the predicted response for a set of
validation samples to the true response obtained from high-fidelity simulations. For scalar outputs, the
statistical measures of accuracy used are the coefficient of determination (), mean error (), and
correlation coefficient () for each sample . These error metrics are computed using a leave-one-out cross
validation approach, in which each sample in the training database is successively removed from the kriging
metamodel and then estimated using all remaining points in the database as the validation samples [9]. The
error between the predicted and true outputs for each of the points is averaged to obtain overall accuracy
statistics of average coefficient of determination () and average mean error (), and average
correlation coefficient (). Better performance is indicated by higher values of and (close to 1)
and lower values of (close to 0).
Accuracy statistics are presented in Table 1. For the second kriging, which approximates response
conditioned on no collapse, the sample experiments which return a high likelihood of collapse ( close
to 1) are removed from the database, since these samples correspond to all earthquake events leading to
collapse or all but a few. In order to limit the sampling error in the median and logarithmic standard deviation
estimates, only samples which had a minimum of 5 non-collapse cases out of 45 total events (imposing a
constraint ) were considered for computing the response output. After this processing, 612
sample experiments remain in the training database for the second kriging. The two surrogate models
demonstrate high prediction accuracy, with the first kriging having an average correlation coefficient of 0.998
for its single output () and the second kriging having an average correlation coefficient of 0.967 over all
16 of its response output values. Table 1 further presents these accuracy statistics for subsets of the output,
where the accuracy of median and logarithmic standard deviation predictions are separately considered for
drifts and accelerations, for response in both horizontal directions for two levels. These metrics demonstrate
that the surrogate models sufficiently capture the variability of outputs with respect to the training database in
order to perform predictions for new observations.
Fig. 3 displays the cross validation results from the second kriging for response, assuming no collapse,
at the height of the cripple wall in the horizontal z direction, where the largest drifts are observed and the onset
of collapse is most likely to occur. There is high correlation between the predicted response, denoted by
and
on the vertical axis, and the true response, denoted by and on the horizontal axis. After
translation of the log output to its original units, greater error can be observed in the estimates of drift than in
estimates of acceleration. The larger error in drift responses can be attributed to the effect of hysteretic
nonlinear behavior on deformation; as the structure is excited, material strength and stiffness degrades under
sustained loading and pulses in the ground motion excitation can cause failure in supporting structural
elements, leading to sudden and large increases in drift values. Due to these effects, the median drift and its
variance are sensitive to even small changes to the input structural model parameters, increasing the complexity
of the surrogate model fitting.
Table 1 – Accuracy statistics of the surrogate models.
Surrogate Model
Response Quantity
Kriging 1
1
700
0.995
5.64%
0.998
Kriging 2
4
612
0.989
0.86%
0.994
4
612
0.829
6.55%
0.910
4
612
0.988
0.76%
0.994
4
612
0.943
5.24%
0.971
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=0.80
=0.50
=0.20
=0.20
=0.50
=0.80
(a)
(b)
Fig. 3 – Correlation between predicted response from the surrogate model and true response from the high-
fidelity simulation for drift (a) and acceleration (b) at the cripple wall level.
The influence of the quality of the cripple wall and earthquake intensity on the probability of collapse
is examined using the first kriging. Fig. 4a displays collapse fragility functions of a building archetype with
varying degrees of cripple wall quality , with function parameters determined by maximum likelihood
estimation (MLE) [17] of predicted points at ten discrete return periods describing the seismic hazard. The
corresponding values of probability of collapse are plotted against spectral acceleration as the intensity
measure used for ground motion selection for each return period. In Fig. 4b, the surrogate predictions of
collapse probabilities at distinct levels of 80%, 50%, and 20% show a linear trend with the cripple wall quality
and earthquake intensity measure. These relationships illustrate the application of the surrogate model in
evaluating the collapse performance of existing wood frame structures of varying degrees of condition or age,
in order to direct vulnerability-based retrofit measures.
Fig. 4 – (a) Fragility functions determined by MLE of predicted collapse probabilities. (b) Earthquake
intensity corresponding to 20%, 50%, and 80% probability of collapse as a function of cripple wall quality.
(a)
(b)
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Fig. 5 demonstrates how the surrogate model may be used to quantify the marginal influence of input
parameters on the output response on the condition of no collapse. Trends in the predicted median drift and
acceleration responses at the cripple wall level are observed for each return period as a function of the cripple
wall quality , floor plan area , and plan aspect ratio . Shaded regions indicate values within one standard
deviation above and below the median prediction based on the kriging uncertainty. For each panel of Fig. 4,
only the x-axis input parameter is variable across the full range of its domain while other input parameters of
the structural model are held constant. It can be observed that the wall material quality and floor plan area have
a greater influence on the deformation of the cripple wall compared to aspect ratio; this is the total
superstructure mass increases proportionally with a larger plan area at a rate which exceeds the relative increase
in total cripple wall length along the perimeter of the building, leading to reduced effective lateral stiffness.
Moreover, there is a larger differential in the drift response as a function of increasing earthquake intensity
compared to the acceleration response. As earthquake intensity increases, indicated by a higher return period,
the uncertainty on the prediction increases due to hysteretic inelastic behavior once yielding is initiated. This
example demonstrates another practical application of the surrogate model, in which rapid estimates of seismic
response is useful for understanding susceptibilities, identifying vulnerable structures, and exploring
alternative structural designs for new construction.
Fig. 5 – Predicted (top) and (bottom) response at the cripple wall level as a function of input parameters
(left to right).
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5. Concluding Remarks
This study examines the performance of kriging metamodeling as a strategy for efficiently approximating the
dynamic response of case study wood frame buildings under earthquake ground motions, in order to enhance
the feasibility of including the contribution of residential wood frame structures to regional-level seismic
performance assessments. Seismic response estimation is demonstrated using an initial set of surrogate models
as a substitute for nonlinear response history analysis. In subsequent steps of the FEMA P-58 methodology for
seismic performance assessments, the response estimates obtained from the surrogate prediction may be used
to assess expected damages, associated consequences, and the performance level of the building. By
quantifying the uncertainty of the response estimates, it is demonstrated that the kriging metamodel has the
additional application of illuminating trends in collapse fragility and peak response with respect to input
structural model properties, with the potential to inform novel methodologies for building assessment and
design iteration.
Solutions are discussed for treating various response outcomes, such as developing separate surrogate
models for collapse probability prediction and seismic response estimation conditioned on no collapse.
However, the exclusion of collapse events leads to disproportionate samples used to compute statistical
measures of the conditional response, introducing error in output variances. To address this issue, a nugget
parameter [18] may be introduced on the log-likelihood profile to ensure global optimality of the kriging
hyperparameters and enhance regression performance. Additional further work would be focused on
improving the robustness and accuracy of the surrogate models, through an intelligent design of experiments
for adaptively selecting additional training samples [8]. Ultimately, a higher-dimensional surrogate model
receiving a greater number of structural properties as input will be refined for investigations of the seismic
performance of a broader range of residential wood frame structures.
6. Acknowledgements
This research was supported by the John A. Blume Earthquake Engineering Center at Stanford University.
The authors are grateful for the access to software and computing resources supported by the National Science
Foundation (Grant Nos. 1520817, 1612843) and the analysis models for the wood frame structures, which
were developed in a Pacific Earthquake Engineering Research (PEER) Center project supported by the
California Earthquake Authority (CEA). All opinions, findings, conclusions or recommendations expressed in
this publication are those of the authors and do not necessarily reflect the views of the research sponsors.
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8d-0014 The 17th World Conference on Earthquake Engineering
© The 17th World Conference on Earthquake Engineering - 8d-0014 -
17th World Conference on Earthquake Engineering, 17WCEE
Sendai, Japan - September 13th to 18th 2020
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Japan.
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process modeling. International Journal for Numerical Methods in Engineering, 114 (5), 501-516.
8d-0014 The 17th World Conference on Earthquake Engineering
© The 17th World Conference on Earthquake Engineering - 8d-0014 -
