The work reported in this thesis is in the area of computational modeling of reliability of engineering structures. The emphasis of the study is on developing methods that are suitable for analysis of large-scale structures such as aircraft structure components. This class of problems continues to offer challenges to an analyst with the most difficult aspect of the analysis being the treatment of nonlinearity in the structural behavior, non-Gaussian nature of uncertainties and quantification of low levels of probability of failure (of the order of 10-5 or less), requiring significant computational effort. The present study covers static/ dynamic behavior, Gaussian/ non-Gaussian models of uncertainties, and (or) linear/ nonlinear structures. The novel elements in the study consist of two components: • application of modeling tools that already exists in the area of design and analysis of computer experiments, and . • application of data based extreme value analysis procedures that are available in the statistics literature. The first component of the work provides opportunity to combine space filling sampling strategies (which have promise for reducing variance of estimation) with kriging based modeling in reliability studies-an opportunity that has not been explored in the existing literature. The second component of the work exploits the virtues of limiting behavior of extremes of sequence of random variables with Monte Carlo simulations of structural response-a strategy for reliability modeling that has not been explored in the existing literature. The hope here is that failure events with probabilities of the order of 10-5 or less could be investigated with relatively less number of Monte Carlo runs. The study also brings out the issues related to combining the above sources of existing knowledge with finite element modeling of engineering structures, thereby leading to newer tools for structural reliability analysis. The thesis is organized into four chapters. The first chapter provides a review of literature that covers methods of reliability analysis and also the background literature on design and analysis of computer experiments and extreme value analysis. The problem of reliability analysis of randomly parametered, linear (or) nonlinear structures subjected to static and (or) dynamic loads is considered in Chapter 2. A deterministic finite element model for the structure to analyze sample realization of the structure is assumed to be available. The reliability analysis is carried out within the framework of response surface methods, which involves the construction of surrogate models for performance functions to be employed in reliability calculations. These surrogate models serve as models of models, and hence termed as meta-models, for structural behavior in the neighborhood of design point. This construction, in the present study, has involved combining space filling optimal Latin hypercube sampling and kriging models. Illustrative examples on numerical prediction of reliability of a ten-bay truss and a W-seal in an aircraft structure are presented. Limited Monte Carlo simulations are used to validate the approximate procedures developed. The reliability of nonlinear vibrating systems under stochastic excitations is investigated in Chapter 3 using a two-stage Monte Carlo simulation strategy. Systems subjected to Gaussian random excitation are considered for the study. It is assumed that the probability distribution of the maximum response in the steady state belongs to the basin of attraction of one of the classical asymptotic extreme value distributions. The first stage of the solution strategy consists of an objective selection of the form of the extreme value distribution based on hypothesis tests, and the next involves the estimation of parameters of the relevant extreme value distribution. Both these steps are implemented using data from limited Monte Carlo simulations of the system response. The proposed procedure is illustrated with examples of linear/nonlinear single-degree and multi-degree of freedom systems driven by random excitations. The predictions from the proposed method are compared with results from large-scale Monte Carlo simulations and also with classical analytical results, when available, from theory of out-crossing statistics. The method is further extended to cover reliability analysis of nonlinear dynamical systems with randomly varying system parameters. Here the methods of meta-modeling developed in Chapter 2 are extended to develop response surface models for parameters of underlying extreme value distributions. Numerical examples presented cover a host of low-dimensional dynamical systems and also the analysis of a wind turbine structure subjected to turbulent wind loads and undergoing large amplitude oscillations. A summary of contributions made along with a few suggestions for further research is presented in Chapter 4.

Monte Carlo simulation techniques have emerged as widely accepted computing tools in tackling many problems in modern structural mechanics. Apart from developments in computational hardware, which have undoubtedly made simulation strategies practically feasible, the success of Monte Carlo simulations has also resulted equally significantly from the methodological developments aimed at controlling sampling variance of the Monte Carlo estimates. The study reported in the present thesis is aimed at developing and validating Monte Carlo simulation based approaches with inbuilt variance reduction capabilities to deal with problems of time variant reliability modeling, random vibration testing, and updating reliability models for statically/dynamically loaded instrumented structures. The relevant literature has been reviewed in Chapter 1. Time variant reliability analysis of randomly parametered and randomly driven non-linear vibrating systems has been tackled by combining two Monte Carlo variance reduction strategies into a single framework (Chapter 2). The first of these strategies is based on the application of the Girsanov transformation to account for the randomness in dynamic excitations and, the second approach is fashioned after the subset simulation method to deal with randomness in system parameters. A novel experimental test procedure to estimate the reliability of structural dynamical systems under excitations specified via random process models has been proposed (Chapter 3). The samples of random excitations to be used in the test are modified by the addition of an artificial control force. An unbiased estimator for the reliability is derived based on measured ensemble of responses under these modified inputs based on the tenets of Girsanov’s transformation. The study observes that an acceptable choice for the control force (that can reduce the sampling variance of the estimator) can be made solely based on experimental techniques. This permits the proposed procedure to be applied in the experimental study of time variant reliability of complex structural systems which are difficult to model mathematically. Illustrative example consists of a multi-axes shake table study on bending-torsion coupled, geometrically non-linear, five-storey frame under uni/bi-axial, non-stationary, random base excitation. The first order reliability method (FORM) and inverse FORM have been extended to handle the problem of updating reliability models for existing, statically loaded structures based on measured responses (Chapter 4). The proposed procedures are implemented by combining Matlab based reliability modules with finite element models residing on the Abaqus software. Numerical illustrations on linear and non-linear frames are presented. A solution strategy within the framework of Monte Carlo simulation based dynamic state estimation method and Girsanov’s transformation for variance reduction has been developed to tackle the problem of updating the reliability of instrumented structures based on measured response under random dynamic loading (Chapter 5). For linear Gaussian state space models, the solution is developed based on continuous version of the Kalman filter, while, for non-linear and (or) non-Gaussian state space models, bootstrap particle filters are adopted. Results from laboratory testing of an archetypal five storey bending-torsion coupled frame under seismic base motions form the basis of one of the illustrative examples. A set of three annexures contain details of numerical methods for discretizing Ito’s differential equations (Annexure 1), working of the Girsanov transformation through Kolmogorov’s equations (Annexure 2) and tools for interfacing Matlab and Abaqus codes (Annexure 3).