He-Qing Mu

Peak Ground Acceleration Estimation by Linear and Nonlinear Models with Reduced Order Monte Carlo Simulation

Abstract: Estimation of the peak ground acceleration (PGA) is one of the main tasks in civil and earthquake engineering practice since it is an important factor for the design spectrum. The Boore–Joyner–Fumal (BJF) and the Crouse–McGuire formula are well-known empirical models by estimating the PGA with the magnitude of earthquake, the fault-to-site distance, and the site foundation properties. It is obvious that a predictive model class with more effective free parameters often fit the data better. However, this does not imply that the complicated formula is more realistic since overfitting may happen when the formula has too many free parameters. In this article, 32 linear and 16 nonlinear predictive model classes are constructed and investigated. The Bayesian model class selection approach is utilized to obtain the most suitable predictive model class for the seismic attenuation formula. In this approach, each predictive model class is evaluated by the plausibility conditional on the data and it is proportional to the evidence which involves a high-dimensional integral. This integral has closed-form solution for the linear model classes. Analytic work was done to improve the original asymptotic expansion in this study. For the nonlinear model classes, the evidence integral can be reduced to two-dimensional and then Monte Carlo simulation is utilized to evaluate the double integral. The most plausible model class is robust in the sense that it balances between the data-fitting capability and the sensitivity to noise. A database of 266 strong-motion records, obtained from the China Earthquake Data Center, is utilized for the analysis. The most plausible predictive model class and its updated model parameters are determined. It turns out that the most plausible model class is generally simpler than the full BJF empirical formula. In the case where no single model class has dominant plausibility, one can utilize the multi-model predictive formula that is a plausibility-weighted average of the prediction of different predictive models.

Real-Time System Identification: An Algorithm for Simultaneous Model Class Selection and Parametric Identification

In this article, a novel Bayesian real-time system identification algorithm using response measurement is proposed for dynamical systems. In contrast to most existing structural identification methods which focus solely on parametric identification, the proposed algorithm emphasizes also model class selection. By embedding the novel model class selection component into the extended Kalman filter, the proposed algorithm is applicable to simultaneous model class selection and parametric identification in the real-time manner. Furthermore, parametric identification using the proposed algorithm is based on multiple model classes. Examples are presented with application to damage detection for degrading structures using noisy dynamic response measurement.

Novel Outlier-Resistant Extended Kalman Filter for Robust Online Structural Identification

AbstractStructural health monitoring (SHM) using dynamic response measurement has received tremendous attention over the last decades. In practical circumstances, outliers may exist in the measurements that lead to undesirable identification results. Therefore, detection and special treatment of outliers are important. Unfortunately, this issue has rarely been taken into systematic consideration in SHM. In this paper, a novel outlier-resistant extended Kalman filter (OR-EKF) is proposed for outlier detection and robust online structural parametric identification using dynamic response data possibly contaminated with outliers. Instead of definite judgment on the outlierness of a data point, the proposed OR-EKF provides the probability of outlier for the measurement at each time step. By excluding the identified outliers, the OR-EKF ensures the stability and reliability of the estimation. In the illustrative examples, the OR-EKF is applied to parametric identification for structural systems with time-varyin...

Ground Motion Prediction Equation Development by Heterogeneous Bayesian Learning

In ground motion prediction, the key is to develop a suitable and reliable GMPE (ground motion prediction equation) characterizing the ground motion pattern of the target seismic region. There are two critical goals encountered in GMPE development. Proposing a suitable predictive formula applicable to target seismic region has attracted much of the attention in previous studies. On the other hand, dependence between prediction–error variance and ground motion data has been observed and the study on this kind of heterogeneous relation becomes an important task yet to be explored. In this article, a novel HEteRogeneous BAyesian Learning (HERBAL) approach is proposed for achieving these two goals simultaneously. The homogeneity assumption on error in the traditional learning approach is relaxed, so the proposed approach is applicable for more general heterogeneous cases. With the generalization made on the traditional Bayesian learning by embedding the derived closed form expression for error variance parameter optimization component into the hyperparameter optimization of ARD (automatic relevance determination) prior, the proposed learning approach is capable of performing continuous model training on a prescribed predictive formula with unknown error pattern. A database of strong ground motion records in the Tangshan region of China is obtained for the analysis. It is shown that the trained optimal model class by the proposed approach is promising as that, the trained optimal model class retains model simplicity of the predictive formula with capability on both robustness enhancement ground motion prediction and precise determination of the error pattern.

Seismic attenuation relationship with homogeneous and heterogeneous prediction-error variance models

Peak ground acceleration (PGA) estimation is an important task in earthquake engineering practice. One of the most well-known models is the Boore-Joyner-Fumal formula, which estimates the PGA using the moment magnitude, the site-to-fault distance and the site foundation properties. In the present study, the complexity for this formula and the homogeneity assumption for the prediction-error variance are investigated and an efficiency-robustness balanced formula is proposed. For this purpose, a reduced-order Monte Carlo simulation algorithm for Bayesian model class selection is presented to obtain the most suitable predictive formula and prediction-error model for the seismic attenuation relationship. In this approach, each model class (a predictive formula with a prediction-error model) is evaluated according to its plausibility given the data. The one with the highest plausibility is robust since it possesses the optimal balance between the data fitting capability and the sensitivity to noise. A database of strong ground motion records in the Tangshan region of China is obtained from the China Earthquake Data Center for the analysis. The optimal predictive formula is proposed based on this database. It is shown that the proposed formula with heterogeneous prediction-error variance is much simpler than the attenuation model suggested by Boore, Joyner and Fumal (1993).

Novel Sparse Bayesian Learning and Its Application to Ground Motion Pattern Recognition

AbstractA novel sparse Bayesian learning for correlated error (SBL-CE) algorithm is proposed to automatically search for an optimal model class with relevance features in regression problems of pat...

Stable Robust Extended Kalman Filter

AbstractIn this paper, a stable and robust filter is proposed for structural identification. This filter resolves the instability problems of the traditional extended Kalman filter (EKF). Instead of ad hoc assignment of the noise covariance matrices in the EKF, the proposed stable robust extended Kalman filter (SREKF) provides real-time updating of the noise parameters. This resolves the well-known instability problem of the EKF due to improper assignment of the noise covariance matrices. Furthermore, the proposed SREKF is capable of removing abnormal data points in a real-time manner. As a result, the parametric identification results will be more reliable and have fewer fluctuations. The proposed approach will be applied to structural damage detection of degrading linear and nonlinear structures in comparison with the plain EKF, utilizing highly contaminated response measurements. It turns out that the estimation error of the state vector and the structural parameters is lower than the EKF by one and tw...

Relevance feature selection of modal frequency-ambient condition pattern recognition in structural health assessment for reinforced concrete buildings

Modal frequency is an important indicator for structural health assessment. Previous studies have shown that this indicator is substantially affected by the fluctuation of ambient conditions, such as temperature and humidity. Therefore, recognizing the pattern between modal frequency and ambient conditions is necessary for reliable long-term structural health assessment. In this article, a novel machine-learning algorithm is proposed to automatically select relevance features in modal frequency-ambient condition pattern recognition based on structural dynamic response and ambient condition measurement. In contrast to the traditional feature selection approaches by examining a large number of combinations of extracted features, the proposed algorithm conducts continuous relevance feature selection by introducing a sophisticated hyperparameterization on the weight parameter vector controlling the relevancy of different features in the prediction model. The proposed algorithm is then utilized for structural health assessment for a reinforced concrete building based on 1-year daily measurements. It turns out that the optimal model class including the relevance features for each vibrational mode is capable to capture the pattern between the corresponding modal frequency and the ambient conditions.

Bayesian Analysis of Peak Ground Acceleration Attenuation Relationship

Estimation of peak ground acceleration is one of the main issues in civil and earthquake engineering practice. The Boore‐Joyner‐Fumal empirical formula [1] is well known for this purpose. In this paper we propose to use the Bayesian probabilistic model class selection approach to obtain the most suitable prediction model class for the seismic attenuation formula. The optimal model class is robust in the sense that it has balance between the data fitting capability and the sensitivity to noise. A database of strong‐motion records is utilized for the analysis. It turns out that the optimal model class is simpler than the full order attenuation model suggested by Boore, Joyner and Fumal (1993).