3.7. Target Spectrum by Surrogate Hazard GP Model

In some cases, users may want to specify the target response spectrum in ground motion selection using a pre-trained surrogate hazard model. This example demonstrates using quoFEM-trained Gaussian Process hazard model to get a target response spectrum at a specific site location in the San Francisco Bay Area given the seismicity from the Hayward Fault.

3.7.1. Pre-trained Gaussian Process Surrogate Model

  1. In this example, the Gaussian Process (GP) model is trained on regional earthquake intensity measure maps that are generated for 147 possible Hayward earthquake scenarios in the UCERF-2 model. For each scenario, the response spectral accelerations at periods from 0.01 sec to 10.0 sec are evaluated for overall 961 sites (31 times 31) in the San Francisco Bay Area. Inter-event and intra-event correlations are considered for all the sites whose median spectra are used as the training dataset.

"A composite image showcasing two different types of graphical data analysis. On the left is a heat map representing data variations over geographic coordinates, with cooler blue shades indicating lower values and warmer red shades indicating higher values. The map is overlaid with a grid and marked by latitude and longitude coordinates, with a color scale on the right-hand side to interpret the data values. On the right is a log-log plot with a dark background, illustrating statistical distributions with a median trend shown in a solid red line and a range indicating plus and minus one standard deviation from the median represented by dashed red lines. The x-axis indicates period (s), while the y-axis represents spectral acceleration (g)."
  1. The training dataset (X.txt and Y.txt) is then loaded in quoFEM to train a GP model where the Longitude and Latitude are input variables and the median response spectrum at that site location is the output. The training takes about 25 sec and shows good performance and accuracy in the cross-validation. The trained model is saved into two files (SimGpModel.json and SimGpModel.pkl) for the use in EE-UQ.

Screenshot of a software interface titled "quoFEM: Quantified Uncertainty with Optimization for the Finite Element Method." The interface includes dropdown menus and file path fields under categories like UQ Engine, FEM, RV, EDP, and RES. The UQ Engine selected is SimCenterUQ with the method category set to "Train GP Surrogate Model." File paths for "Training Points (Input) File" and "System Results (Output) File" are displayed, alongside an option to 'Choose' files. A checkbox for "Advanced Options for Gaussian Process Model" and a note stating "Any information entered on the FEM tab will be ignored" are visible at the bottom.
Screenshot of a software interface displaying a summary of surrogate modeling results with goodness-of-fit statistics and a leave-one-out cross-validation (LOOCV) prediction scatter plot. The summary indicates the modeling has been completed with 193 training samples, 0 model simulations, and an analysis time of 25.1 seconds. The goodness-of-fit section shows values for normalized error (NRMSE) ranging from 0.030 to 0.076 and corresponding R-squared (R2) values from 0.854 to 0.984 across different variables labeled sa_1 through sa_13. The scatter plot depicts a close alignment of predicted responses (LOOCV) against exact responses, with the points closely huddled along the diagonal line, suggesting a strong predictive performance.

3.7.2. Configure Surrogate Target Spectrum

  1. Navigate to the EVT tab and select the PEER NGA Records as the Load Generator. In this example we use the Spectrum from Hazard Surrogate as the Target Spectrum (specified in the dropdown list).

  2. Click Choose buttons to select and load the SimGpModel.json and SimGpModel.pkl files as the hazard surrogate GP model.

  3. In the Intensity Measure Periods (sec): textbox, fill in the periods for the response spectral accelerations which are “0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 1, 2, 3, 4, 5, 7.5, 10” in this example.

  4. Two random variables (“RV_column1” and “RV_column2”) are automatically populated from the loaded surrogate model, and users can specify the desired site location to evaluate the target response spectrum.

Screenshot of a software interface for generating a target spectrum. The interface includes fields for Type (selected as "Spectrum from Hazard Surrogate"), file path input for Hazard SurrogateGP Info and Model with "Choose" buttons next to each, and a selection of options such as "Maximum Allowable Normalized Variance" and "Intensity Measures". There is also a dropdown menu for "GP output" and a list for "Intensity Measure Periods (secs)". Below is a section titled "Input Random Variables" with numerical values listed, and a button labeled "Get Spectrum" at the bottom.
  1. Once the above configurations are set up, click Get Spectrum button which will launch backend surrogate applications to predict the response spectrum at the provided location. Note although this example shows the application for predicting the response spectrum at a given location, the surrogate model can be trained on other input variables (not necessarily Longitude and Latitude).

  2. Once the prediction is completed, the Target Spectrum widget will automatically switch to User Specified option with the tabulated response spectrum predicted for the given input variables.

Screenshot of a software interface titled "Target Spectrum," showing a table with two columns labeled "T [sec.]" and "SA [g]", with rows of values under each heading. These rows correspond to different time periods in seconds and spectral acceleration in g. The interface includes buttons labeled "Add," "Remove," and "Load CSV" at the bottom, and a dropdown menu at the top right with the option "User Specified" displayed.

3.7.3. Select Ground Motion and Run Analysis

  1. Once the target response spectrum is available, users can follow the same procedure as introduced in EE-UQ Example 3 to select and scale ground motion records.

Screenshot of an earthquake engineering software interface with various panels. On the left, a "Target Spectrum" panel shows a table with two columns labeled "T [sec.]" and "SA [g]" with numerical values. Below it is an "Output Directory" section and a "Ground Motion Components" list detailing earthquake records with columns like "RSN," "Scale," "Earthquake," and "Station." The top right panel is titled "Record Selection" with fields for specifying the number of records, fault type, magnitude range, and other seismic parameters. The main graph to the right displays a "Response Spectra" chart with multiple curves representing spectral acceleration over periods and shows mean, standard deviation, target, and selected response spectra.
  1. In the example, a simple SDOF model is used in SIM tab to demonstrate the structural analysis step and default configurations are used in the FEM and EDP tabs.

Screenshot of a software interface titled "Building Model Generator" with input fields for building information such as Number of Stories, Floor Weights, Story Stiffness, and Yield Strength in X and Y directions. A simple line diagram representing a building structure is displayed on the right side of the interface.
The image shows a user interface for an FE (Finite Element) Application, presumably from a software used for structural analysis or similar engineering computations. The interface includes options for setting up a transient analysis with OpenSees, defining numerical integration parameters, selecting an algorithm (Newton), specifying convergence tests, solvers, damping models, damping ratios, and selecting tangent stiffness options. There is also an input field for an analysis script and a "Choose" button, possibly for loading or confirming settings.
A screenshot of a user interface with a misspelled title reading "Engineering Demand Paramater Generator" instead of "Parameter," with a dropdown menu option labeled "Standard Earthquake."
  1. By clicking Run button, one can launch the analysis and the application will automatically switch to the RES tab once the analysis is completed. One could navigate to the Data Value panel to visualize and save the new realizations.

A screenshot of a spreadsheet containing statistical data. There are columns for "Summary," "Name," "Mean," "StdDev" (standard deviation), "Skewness," and "Kurtosis" with various numerical values listed for each category. The rows are categorized by different sections such as UQ, GI, SIM, EVT, FEM, EDP, RV, and RES, each with specific entries like "1-PFA-0-1," "1-PFA-0-2," "1-PFA-1-1," and so on, followed by their corresponding statistical measurements.
Screenshot of a computer interface showing a scatter plot on the left with data points labeled 'Run # 1' along the horizontal axis and 'HP-R' on the vertical axis. A single red data point is highlighted among blue data points. The right side of the image displays a data table titled 'MultipleEvent' with columns including 'Run #', '1-PFA-0-1', '1-PFA-0-2', '1-PFA-1-1', '1-PFA-1-2', '1-PFD-1-1', '1-PFD-1-2', '1-PID-1-1', and '1-PRD-1-1', among others. Each row corresponds to a numbered run with various numerical values. The top of the interface offers options to 'Save Table', 'Save Columns Separately', 'Save RVs', and 'Save QoIs'.