Application of Subset Simulation to Seismic Risk Analysis

This paper presents the application of a new reliability method called Subset Simulation to seismic risk analysis of a structure, where the exceedance of some performance quantity, such as the peak interstory drift, above a specified threshold level is considered for the case of uncertain seismic excitation. This involves analyzing the well-known but difficult first-passage failure problem. Failure analysis is also carried out using results from Subset Simulation which yields information about the probable scenarios that may occur in case of failure. The results show that for given magnitude and epicentral distance (which are related to the ‘intensity’ of shaking), the probable mode of failure is due to a ‘resonance effect.’ On the other hand, when the magnitude and epicentral distance are considered to be uncertain, the probable failure mode correspondsto the occurrence of ‘large-magnitude, small epicentral distance’ earthquakes

Rare event simulation in finite-infinite dimensional space

Modern engineering systems are becoming increasingly complex. Assessing their risk by simulation is intimately related to the efficient generation of rare failure events. Subset Simulation is an advanced Monte Carlo method for risk assessment and it has been applied in different disciplines. Pivotal to its success is the efficient generation of conditional failure samples, which is generally non-trivial. Conventionally an independent-component Markov Chain Monte Carlo (MCMC) algorithm is used, which is applicable to high dimensional problems (i.e., a large number of random variables) without suffering from ‘curse of dimension’. Experience suggests that the algorithm may perform even better for high dimensional problems. Motivated by this, for any given problem we construct an equivalent problem where each random variable is represented by an arbitrary (hence possibly infinite) number of ‘hidden’ variables. We study analytically the limiting behavior of the algorithm as the number of hidden variables increases indefinitely. This leads to a new algorithm that is more generic and offers greater flexibility and control. It coincides with an algorithm recently suggested by independent researchers, where a joint Gaussian distribution is imposed between the current sample and the candidate. The present work provides theoretical reasoning and insights into the algorithm

Comparison of uncertainty in modal identification under known and unknown input excitations

Modal identification is a technique that can assess modal properties of structures based on vibration data. This technique can be categorized into known and unknown input modal identification. Known input modal identification, e.g. forced vibration tests, is more economically demanding because of the need of special devices to generate artificial loading but the data obtained has higher signal-to-noise ratio. Unknown input modal identification, e.g. ambient vibration, could be performed economically with structures under working conditions. This study employs a fast Bayesian FFT method to not only identify the modal parameters, such as natural frequencies and damping ratios, but also quantify the uncertainties associated with the modal identification results. This provides a tool to investigate the uncertainties in the modal identification. In this study two numerical examples are used to generate synthetic data for investigating and comparing the uncertainties in the known and unknown input modal identification

On the solution of first excursion problems by simulation with applications to probabilistic seismic performance assessment

In a probabilistic assessment of the performance of structures subjected to uncertain environmental loads such as earthquakes, an important problem is to determine the probability that the structural response exceeds some specified limits within a given duration of interest. This problem is known as the first excursion problem, and it has been a challenging problem in the theory of stochastic dynamics and reliability analysis. In spite of the enormous amount of attention the problem has received, there is no procedure available for its general solution, especially for engineering problems of interest where the complexity of the system is large and the failure probability is small. The application of simulation methods to solving the first excursion problem is investigated in this dissertation, with the objective of assessing the probabilistic performance of structures subjected to uncertain earthquake excitations modeled by stochastic processes. From a simulation perspective, the major difficulty in the first excursion problem comes from the large number of uncertain parameters often encountered in the stochastic description of the excitation. Existing simulation tools are examined, with special regard to their applicability in problems with a large number of uncertain parameters. Two efficient simulation methods are developed to solve the first excursion problem. The first method is developed specifically for linear dynamical systems, and it is found to be extremely efficient compared to existing techniques. The second method is more robust to the type of problem, and it is applicable to general dynamical systems. It is efficient for estimating small failure probabilities because the computational effort grows at a much slower rate with decreasing failure probability than standard Monte Carlo simulation. The simulation methods are applied to assess the probabilistic performance of structures subjected to uncertain earthquake excitation. Failure analysis is also carried out using the samples generated during simulation, which provide insight into the probable scenarios that will occur given that a structure fails