STATISTICAL BASED NON-LINEAR MODEL UPDATING USING FEATURE EXTRACTION Page: 4 of 14
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STATISTICAL BASED NON-LINEAR MODEL UPDATING
USING FEATURE EXTRACTION
John F. Schultze, Francois M. Hemez, Scott W. Doebling, and Hoon Sohn
Engineering Analysis Group (ESA-EA), M/S P946
Los Alamos National Laboratory
Los Alamos, New Mexico 87545
This research presents a new method to improve analytical
model fidelity for non-linear systems. The approach
investigates several mechanisms to assist the analyst in
updating an analytical model based on experimental data
and statistical analysis of parameter effects. The first is a
new approach at data reduction called feature extraction.
This is an expansion of the update metrics to include specific
phenomena or character of the response that is critical to
model application. This is an extension of the classical
linear updating paradigm of utilizing the eigen-parameters or
FRF's to include such devices as peak acceleration, time of
arrival or standard deviation of model error. The next
expansion of the updating process is the inclusion of
statistical based parameter analysis to quantify the effects of
uncertain or significant effect parameters in the construction
of a meta-model. This provides indicators of the statistical
variation associated with parameters as well as confidence
intervals on the coefficients of the resulting meta-model.
Also included in this method is the investigation of linear
parameter effect screening using a partial factorial variable
array for simulation. This is intended to aid the analyst in
eliminating from the investigation the parameters that do not
have a significant variation effect on the feature metric.
Finally an investigation of the model to replicate the
measured response variation is examined
The recommended "Standard Notation for Modal Testing &
Analysis" is used throughout this paper, see Reference [1.] .
Current model updating methods in structural dynamics are
general based on linear assumptions and do not have a
quantifiable confidence index of model components. Several
methods use either the measured eigen-parameters or
FRFs. These techniques commonly attempt to either map
the experimental information to the model space or the
converse. This results in a confounding of system
information through the data expansion or condensation.
Identified errors are associated with specific parameters or
physical regions of a model. There is normally little
evaluation, from either a Design of Experiments (DoE) or
statistical approach to quantify the model update mechanism
for a range of applications and confidence intervals
A new method based on use of response 'features' and a
DoE approach parameter variation to updating analytical
models. This method is applicable to time-varying non-linear
systems where classical methods often do not succeed.
This method also provides for confidence indications of
A 'feature' is an identified quantity from the response data.
This could be as simple as the peak level of a single
response record to a more coupled metric such as the
standard deviation of model error over the entire response
space. The former is one of the metric evaluated in this
paper and the latter is currently under investigation for a
different model. A 'feature', by its nature, is a general term
and is specified by the analyst. Under this guideline the
traditional update choices of eigen-parameters would qualify
though their application is only meaningful for linear-
A flowchart of the proposed method is shown in Figure 1.
This development in this paper will follow this guide. The
method is iterative in nature and the selection of features is
dependent on the analyst's goals and insights. In some
instances, iterations will be performed within steps and in
most cases at least some redefinition/refinement of
parameters and their levels is necessary.
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Schultz, J.F. & Hemez, F.M. STATISTICAL BASED NON-LINEAR MODEL UPDATING USING FEATURE EXTRACTION, article, October 1, 2000; New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc723374/m1/4/: accessed April 20, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.