Modeling and Simulation of Nonstationary Ground Motions

PROJECT GOALS AND OUTCOMES

Establishment of reliable seismic design guidelines requires reasonable estimates of the seismic loads that a structure will experience during its service life.  Earthquake ground motions are produced by complex processes that are not yet fully understood. The gaps in our understanding of the involved physical mechanisms, coupled with the lack of a sufficient number of recordings from a wide variety of seismological conditions have challenged the task of ground motion estimation. As a result, traditional ground motion models have relied on simplistic equations that are based on a set of strong assumptions. Recent advances in computer technology and the growth in seismic databases have led to an increased interest in data-driven modeling approaches where the relationship between input and output is inferred from the observed data, without using a fixed, parametric equation.

This research sought answers to the following questions: (1) Can a data-driven model reliably estimate the ground motion from a scenario earthquake dominating the seismic hazard at a given site? (2)Which seismic predictors should be included in the model? (3) Can the prediction uncertainty be quantified in a manner accessible to researchers and engineers not well-versed in data-driven modeling?

Our findings showed that data-driven ground motion modeling is a viable alternative to its traditional counterparts. We used cross validation to identify the set of predictors to be included in the model. The selected variable set depends on the amount of information provided by each candidate predictor, as well as the information shared by different predictor subsets. For a special case of the data-driven model where we allowed incorporation of known relationships between a subset of predictors and the modeled quantity, we derived analytical equations for confidence and prediction intervals. For more general settings, we used Bayesian inference to quantify prediction uncertainty.

The methodology we followed in this project was aimed at fuller utilization of information contained in seismic records facilitating construction of improved ground motion models, ultimately, enabling more accurate assessment of the performance of the nation’s critical infrastructure in future earthquakes.

This project is highly interdisciplinary, drawing from earthquake engineering, machine learning, classical and Bayesian statistics, data mining, and information theory.  Since, at a broad level, this project addresses the problem of extracting meaningful patterns from empirical data, the findings are relevant to a wide array of disciplines encompassing engineering, science, and medicine where predictive modeling is of interest.

This project funded three graduate students, one of which has earned a PhD degree. The Principal Investigator introduced and taught a graduate level course on reliability, and the Co-PI used project findings in course projects. We disseminated our findings through journal publications and conference presentations.

PUBLICATIONS & PRESENTATIONS

• J. Tezcan, Y. Dak Hazirbaba and Q. Cheng (2015). A Kernel-based Mixed Effect Regression Model for Earthquake Ground Motions. Advances in Engineering Software (in review).

• Y. Dak Hazirbaba and J. Tezcan (2015). Image-based Modeling and Prediction of Nonstationary Ground Motions. Computers & Structures (accepted).

• J. Tezcan, J. Cheng and Q. Cheng (2015). Prediction of Nonstationary Ground Motions as Time-Frequency Images. IEEE Transactions on Geoscience and Remote Sensing (accepted).

• Q. Cheng, J. Tezcan and J. Cheng (2014). Confidence and Prediction Intervals for Semiparametric Mixed-Effect Least Squares Support Vector Machine. Pattern Recognition Letters, 40:88-95.

• J. Tezcan, Y. Dak Hazirbaba and Q. Cheng (2014) A Semi-parametric Regression Tool for Seismic Risk Management Applications. Proceedings of the 3^rd International Conference on Urban Disaster Reduction, September 28- October 1, Boulder, Colorado.

• Y. Dak Hazirbaba and J. Tezcan (2014).  A Novel Approach for Modeling Nonstationary Ground Motions. Proceedings of the 12^th International Conference on Computational Structures Technology, September 2-5, Naples, Italy.

• J. Tezcan, Y. Dak Hazirbaba and Q. Cheng (2014).  Least-Squares-Kernel-Machine Regression for Earthquake Ground Motion Prediction. Proceedings of the 12^th International Conference on Computational Structures Technology, September 2-5, Naples, Italy.

• J. Tezcan and Q. Cheng (2012). A Nonparametric Characterization of Vertical Ground Motion Effects. Earthquake Engineering and Structural Dynamics, 41(3), p.515-530.

• Tezcan, Jale, Cheng, Qiang (2012). Support vector regression for estimating earthquake response spectra.  Bulletin of Earthquake Engineering. 10 (4), 1205-1219.

• Y. Dak Hazirbaba, J. Tezcan, J., Q. Cheng (2012). Poster Presentation: Maximum direction to geometric mean spectral response ratios using the relevance vector machine. NSF CMMI Engineering Research and Innovation Conference, Boston, MA.

• J. Tezcan and Q. Cheng (2012). Poster Presentation: A Bayesian approach for modeling and simulation of non-stationary ground motions. NSF CMMI Engineering Research and Innovation Conference, Boston, MA.

• J. Tezcan, Y. Dak Hazirbaba and Q. Cheng (2012) Maximum Direction to Geometric Mean Spectral Response Ratios using Relevance Vector Machines. Proceedings of the 15^th World Conference on Earthquake Engineering, Sept 24-28, Lisbon, Portugal.

RESOURCES

Animated response of a single-degree-of-freedom system

Matlab files: Save the Main*.m file and the data.mat file (if any) in the same folder, and execute the main file.

• Free vibration:  Main_free_vibration.m 

• Earthquake response, base fixed:  Main_fixed_base.m   data.mat

• Earthquake response, base moving with ground:  Main_moving_base.m   data.mat

• Response spectrum:  Main_Response_Spec   data.mat

Wavelet Transform

• Continuous wavelet transform with complex Morlet wavelet:  Morlet1   data.mat

 Probability, Statistics and Reliability

   Matlab codes are provided inside the document.

• Construction of confidence intervals

• An introduction to Monte Carlo simulations 

  CONTACT INFORMATION

This material is based upon work supported by the National Science Foundation under Grant Number CMMI 1100735.                  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily    reflect the views of the National Science Foundation.