Jale Tezcan

Confidence and prediction intervals for semiparametric mixed-effect least squares support vector machine

We consider estimating the confidence and prediction intervals for semiparametric mixed-effect least squares support vector machine (LS-SVM). Explicit formulas are derived for confidence and prediction intervals. The accuracy of the derived analytical equations is assessed by comparing with wild cluster bootstrap-t method on simulated and real-world data with different levels of random-effect and residual variances, and different numbers of clusters. Close match between the derived expressions and the bootstrap results is observed.

Support vector regression for estimating earthquake response spectra

This study uses support vector regression (SVR), a supervised machine learning algorithm, to model the average horizontal response spectrum as a nonparametric function of a set of predictor ground motion variables. Traditional ground motion prediction equations (GMPEs) are derived using parametric regression, where a fixed functional form is selected, and the model coefficients are determined by minimizing the errors on the training set. The SVR model is nonparametric; there is no need to assume a fixed functional form. Using nonlinear basis functions, the data points are mapped into a high dimensional feature space, where nonlinear input-output relationships can be expressed as a linear combination of nonlinear functions, using a subset of the data points. The combination weights are determined by minimizing the generalization error, using a formal mechanism to characterize the trade-off between the model complexity and the quality of fit to the data. Minimization of the generalization error instead of the fitting error leads to better generation to unseen data, and thus reduces the risk of over-fitting for a given number of data points. The SVR model is not based on a specific probability distribution, and is readily applicable to non-Gaussian data. An example application is presented for vertical strike-slip earthquakes, and the predictions from the SVR model are compared to the recently developed GMPEs. The results demonstrate the validity of the proposed model, and suggest that it can be used as an alternative to the conventional ground motion prediction models.

A Probabilistic Nonparametric Model for the Vertical-to-Horizontal Spectral Ratio

This article develops a probabilistic nonparametric model for the vertical-to-horizontal spectral ratio of earthquake ground motions. Using Relevance Vector Machines, the spectral ratio is characterized based on ground motion records. Unlike conventional models, the proposed method does not require a functional form, and treats the model coefficients as random variables instead of fixed quantities. Demonstrative examples using records from strike-slip earthquakes are presented, and the results are compared to those from the conventional empirical models. The proposed model provides reasonably good estimates using only three predictive variables: magnitude, distance, and shear wave velocity. Future studies will investigate near-fault ground motions.

A short-term assessment of a multi-faceted engineering retention program

A set of formative tools have been designed to assess the short-term progress of a multi-faceted program aimed at improving the overall graduation rate from 37 to 67 percent over a five-year period at a College of Engineering. The holistic program consists of a set of academic and non-academic components designed to improve first- and second-year retention rates to 80 and 90 percent, respectively. Using selective performance indicators, each program component is assessed to determine its impact on the programs short-term progress. The assessment shows that the student support offered by the program components has a positive impact on the number of enrolled engineering majors. Following one year of implementation, the program is approximately half way towards reaching its target retention rates. The program has also unexpectedly and positively impacted student recruitment and campus-wide retention efforts. A key lesson learned through project implementation is that strategic assessment of activities is crucial not only to determine the extent to which the desired objectives have been met but to also refine the program components to achieve the desired retention goals. Furthermore, the efforts which focus on first-year students should not overlook the fact that parental/guardian consent may be required as part of assessment activities.

A Multiway Model for Predicting Earthquake Ground Motion

This paper develops a novel supervised method for predicting earthquake ground motions in the wavelet domain. The training input is a set of seismological predictors related to seismic source, path and local site conditions, and the training output consists of the weights from a multiway analysis of ground motions. We treat wavelet transforms of acceleration records as images and extract essential patterns from them using tensor decomposition. The decomposition weights of these patterns are then linked to seismological variables using general regression neural network (GRNN). The resulting nonparametric model is then used to predict the wavelet image of an accelerogram for a given set of seismological variables. The predicted image can be transformed back to the time domain using inverse wavelet transform for subsequent processing to match a given design spectrum. Unlike conventional ground motion models, the proposed approach retains the time domain characteristics of ground motions. Pearsons correlation coefficient between the vectorized forms of actual and predicted wavelet images has been used as the similarity metric in assessing the prediction capability of the resulting model. Experimental results demonstrate the ability of the proposed model to predict significant patterns in the seismic energy distribution.

A kernel-based mixed effect regression model for earthquake ground motions

Abstract This paper presents a semi-parametric mixed-effect regression approach for analyzing and modeling earthquake ground motions, taking into account the correlations between records. Using kernels, the proposed method extends the classical mixed model equations to complicated relationships. The predictive equation is composed of parametric and nonparametric parts. The parametric part incorporates known relationships into the model, while the nonparametric part captures the relationships which cannot be cast into a simple parametric form. A least squares kernel machine is used to infer the nonparametric part of the model. The resulting semi-parametric model combines the strengths of parametric and nonparametric approaches, allowing incorporation of prior, well-justified knowledge into the model while retaining flexibility with respect to the explanatory variables for which the functional form is uncertain. Equations for pointwise confidence and prediction intervals around the conditional mean are provided. The validity of the proposed method is demonstrated through numerical simulations and using recorded ground motions.

Modeling and Prediction of Nonstationary Ground Motions as Time–Frequency Images

Proper modeling of nonstationary characteristics of ground motions is critical in estimating the seismic performance of structures. The importance of ground motion nonstationarity is being increasingly recognized in seismic design codes and provisions. This paper develops a new method for predicting seismic ground motions in the joint time–frequency domain based on recorded ground motions. We treat wavelet energy maps of acceleration records as images and extract essential patterns from them using principal component analysis. These patterns are then linked to the seismic source, path, and site variables using general regression neural network. The resulting model predicts an image representing the expected evolutionary power spectrum conditioned on the input variables. An example application is presented using records from the Next Generation Attenuation of Ground Motions Database of the Pacific Earthquake Engineering Center. As opposed to conventional ground motion prediction models, the proposed approach retains the time domain characteristics of ground motions. The results show that the proposed model can predict significant patterns in the seismic energy distribution, acceleration time series, and 5% damped elastic spectral accelerations.

Least-Square-Support-Vector-Machine-based approach to obtain displacement from measured acceleration

A kernel regression approach is proposed for obtaining the displacement time series from a recorded acceleration time series.The proposed method does not require any baseline adjustment, other than removing the mean of the accelerogram record.The solution obtained is numerically stable and thus regularization is not necessary.The reconstructed displacement does not exhibit any long period drift. Recent advances in computer and sensing technologies have led to the proliferation of sensor networks in structural health monitoring and condition monitoring applications.Vibration data collected by sensors provide useful information about the condition of a structure or a machine component, facilitating identification of any changes in its performance. While acceleration and displacement data provide complementary information, a cost-effective alternative to monitoring both is to estimate displacements from accelerations. This paper presents a kernel regression approach for obtaining displacement time series from acceleration data. Starting from a second-order central difference approximation, the method performs ridge regression in a feature space induced by the linear kernel. The main advantages of the proposed method are (1) It does not require baseline adjustment, other than removing the mean of the acceleration record; (2) The solution obtained is numerically stable, and thus regularization is not necessary; (3) The reconstructed displacement does not exhibit any long period drift. The validity of the proposed method is demonstrated through examples, where structural systems displacements computed using the proposed approach were compared to the recorded experimental displacements. While the presented examples focus only on monitoring of vibrations responses of structural systems, the proposed method can be used in other settings where a displacement signal is to be estimated from an acceleration signal with appropriate, application-specific modifications.