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Earthquake Engineering (EE-UQ) / Re: Validating the Surrogate Model
« on: June 16, 2023, 01:24:49 AM »
Hi Gaurav,
Good questions and thanks so much for the interest of using the surrogate modeling in EE-UQ and quoFEM! I'm trying to first brief a potential use case of the PLoM package in EE-UQ/quoFEM and then write my thoughts to your questions - hope they could be helpful if any.
Let's consider the uncertainty in earthquake source, path, and local soil condition, one would except different ground motions given a specific return period. If we select a set of representative ground motions and use them for response history analysis of the structure, the ground motion uncertainty is propagated to the uncertainty in the resulting structural responses. Let's assume one ground motion could be described by a set of M intensity measures (e.g., PGA, PSA...) and we're interested in P different responses (e.g., peak displacement/peak acceleration), a (M+P)xN matrix can be constructed (with N realizations). The PLoM package could help on two possible tasks: (1) it can learn this matrix and generate new realizations that preserve the data structure and (2) it can generate new realizations in which a few dimensions have moments per user-defined values (e.g., the mean Sa of input matrix is 0.6g while the mean Sa of new realizations is moved to 0.4g) by adding corresponding constraints (e.g., the target mean Sa, 0.4g). So, the PLoM package develops a mapping between the joint distributions of input parameters and output responses (e.g., mapping a sample of PSA to a sample of responses).
> For the first question, it may not be straightforward to validate one PLoM realization at a particular SAavg (it's a single realization given the SAavg though one could potentially generate sufficient sets of PLoM realizations and then estimate the statistics); alternatively, it's more easier to validate one set of PLoM realizations at a particular mean SAavg - one could first compute the mean SAavg of the validation set and provide that as a constraint, then the comparison would be made between the statistics of the responses from PLoM and the validation set.
> For the second question, if I understand correctly, ground motion selection/scaling (e.g., https://www.nist.gov/publications/selecting-and-scaling-earthquake-ground-motions-performing-response-history-analyses) seems what you were asking for. Given the target intensity measures (e.g., PSA), one could select recordings that fit the target intensity measures, and spectral matching algorithms may also be considered if desired.
> For the LOOCV, similar to the first questions, it may not be straightforward to do one data point (PLoM is intended to focus on the joint distribution instead of individual points).
Hope the above discussion could be helpful if any and please do feel free to get us back if you have any trouble of running the PLoM package and/or have any needs that we could help on to extend/gear the package better for your use case.
Regards,
Kuanshi
Good questions and thanks so much for the interest of using the surrogate modeling in EE-UQ and quoFEM! I'm trying to first brief a potential use case of the PLoM package in EE-UQ/quoFEM and then write my thoughts to your questions - hope they could be helpful if any.
Let's consider the uncertainty in earthquake source, path, and local soil condition, one would except different ground motions given a specific return period. If we select a set of representative ground motions and use them for response history analysis of the structure, the ground motion uncertainty is propagated to the uncertainty in the resulting structural responses. Let's assume one ground motion could be described by a set of M intensity measures (e.g., PGA, PSA...) and we're interested in P different responses (e.g., peak displacement/peak acceleration), a (M+P)xN matrix can be constructed (with N realizations). The PLoM package could help on two possible tasks: (1) it can learn this matrix and generate new realizations that preserve the data structure and (2) it can generate new realizations in which a few dimensions have moments per user-defined values (e.g., the mean Sa of input matrix is 0.6g while the mean Sa of new realizations is moved to 0.4g) by adding corresponding constraints (e.g., the target mean Sa, 0.4g). So, the PLoM package develops a mapping between the joint distributions of input parameters and output responses (e.g., mapping a sample of PSA to a sample of responses).
> For the first question, it may not be straightforward to validate one PLoM realization at a particular SAavg (it's a single realization given the SAavg though one could potentially generate sufficient sets of PLoM realizations and then estimate the statistics); alternatively, it's more easier to validate one set of PLoM realizations at a particular mean SAavg - one could first compute the mean SAavg of the validation set and provide that as a constraint, then the comparison would be made between the statistics of the responses from PLoM and the validation set.
> For the second question, if I understand correctly, ground motion selection/scaling (e.g., https://www.nist.gov/publications/selecting-and-scaling-earthquake-ground-motions-performing-response-history-analyses) seems what you were asking for. Given the target intensity measures (e.g., PSA), one could select recordings that fit the target intensity measures, and spectral matching algorithms may also be considered if desired.
> For the LOOCV, similar to the first questions, it may not be straightforward to do one data point (PLoM is intended to focus on the joint distribution instead of individual points).
Hope the above discussion could be helpful if any and please do feel free to get us back if you have any trouble of running the PLoM package and/or have any needs that we could help on to extend/gear the package better for your use case.
Regards,
Kuanshi