Abstract

The analysis of structures under random dynamic excitations, such as earthquake loads, requires realistic stochastic modeling of the excitations as well as numerically efficient simulation techniques. Evolutionary power spectra (EPS) provide an appealing model for capturing the statistics and the time-varying frequency content of the underlying non-stationary stochastic processes. Further, they can be used as a basis for joint time-frequency system response analysis, or efficient stochastic simulation utilizing advanced Monte Carlo techniques. Several approaches exist for estimating EPS based on time records, among which, wavelet-based approaches appear to have received particular attention. To obtain a reliable estimate of an EPS, a significant amount of data and/or some prior knowledge of the underlying physics of the process are required. However, in several engineering applications large amounts of data can be difficult to acquire for several reasons, such as cost (e.g. expensive sensor maintenance), frequency and unpredictability of the effect (e.g. earthquakes), and sensor failures. Further, available data can be highly limited and irregularly sampled. Hence, the EPS estimation needs to cope with fragmentary and incomplete data records, i.e. missing data. In this regard, most spectral analysis techniques, at least in their standard implementation, are not capable of addressing this challenge. To address the problem of missing data in EPS estimation, a neural network based approach has been developed in Comerford et al. (2014) which is adapted and applied herein specifically to the analysis of earthquake records with various missing data characteristics (e.g. missing individual data points and/or data sequences). All characteristics are investigated for various amounts of missing data, up to 50%. The neural network is employed to capture the stochastic pattern in the available data in an “average sense”. The trained network, having stored process trends within its connection weights, is then exploited for generating new data to fill sampling gaps compatible with the underlying stochastic process. Finally, EPS estimates are derived by utilizing recently developed wavelet based approaches. The influence of missing data on results of stochastic structural response and reliability analyses is investigated for a real-size structure under earthquake excitation. In particular, a nonstationary ground acceleration process defined in terms of the Clough-Penzien spectrum is used to generate synthetic ground motions. Based on these records, several scenarios with respect to the characteristics and magnitude of missing data are constructed. Then, the analysis with the estimated EPS’s is compared to the results obtained by using directly the original evolutionary power spectrum (based on the Clough-Penzien spectrum). In the example, a large Finite Element model of a multi-story building with vibration control devices that exhibit nonlinear hysteretic behavior is analyzed. The maximum interstory drift is used as a representative response measure of the structure for the comparative study. In addition, the structural reliability is estimated for the investigated scenarios. In all cases, a very strong correlation was found between responses obtained from samples by using the original evolutionary power spectrum and the estimated spectrum with missing data. This indication of high-quality results is supported by the results of the reliability assessment with missing data, which are also in very good agreement with the results derived using the original evolutionary power spectrum