Vibration testing of structures constitutes a crucial step in design and commissioning of engineering structures. The focus here is on simulating field conditions in a laboratory so that detailed investigations of the structural behavior under various future load scenarios can be carried out. A major enabling technology in recent years in this field of study, especially, in the context of earthquake engineering, and automotive testing, has been the development of servo-hydraulic actuation systems, which form the principal component of test facilities, such as, multi-axes shake tables for testing building structures under earthquake loads, multi-post testrigs for testing vehicles subjected to road loads, and reaction-wall based test systems for simulating horizontal effects of earthquake loads on building structures. These systems have enabled the conduct of systematic studies on simulation of nonlinear structures under transient loads, simulation of multi-component and spatially varying random loads, and combining numerical and experimental methods with a view to avoid scaling while testing small scale critical components of large built-up structures. The investigations reported in this thesis are in this area of research and are primarily aimed at exploring the potential of servo-hydraulic test systems to address a few intricate issues related to performance assessment of engineering vibrating systems. A broad-based overview of goals of experimental approaches in vibration engineering, including dynamic system characterization and performance assessment, is presented in Chapter 1. Also discussed are the brief details of vibration testing methods developed in the context of earthquake engineering (including quasi-static test, effective force test, shake table test, combined effective force and shake table test, various versions of pseudo-dynamic test, and real-time substructuring) and automotive vehicle testing (including input excitation based methods and response based methods). The discussion notes the remarkable success witnessed in combining mathematical methods and experimental techniques especially in problems of characterization of dynamic system properties. Similar success, however, is observed to be not wide-spread in the context of development of test methods aimed at performance assessment of vibrating systems. The review culminates with the identification of the following three problems to be tackled in the present thesis: (a) development of efficient experimental procedures to estimate time varying reliability of structures under multi-component earthquake loads and similar analysis of vehicle structures under spatially varying random road loads; the focus here is on achieving sampling variance reduction in estimating the reliability; (b) development of experimental procedures to determine optimal cross-power spectral density models of partially specified multi-component random loads so as to produce the highest and lowest response variance in a specified response variable; the focus here is on seismic tests of asymmetric structures under partially specified multi-component earthquake loads, and on characterizing optimal correlations between two parallel tracks which maximize or minimize the vehicle response; and (c) development of a modified pseudo-dynamic test procedure, to incorporate additional components in numerical and experimental modeling in terms of an augmented linearized variational equation, so as to assess and contain propagation of numerical and experimental errors. The subsequent three chapters of the thesis tackle these questions and in doing so the thesis makes the following contributions: (A) Inspired by the Girsanov transformation based Monte Carlo simulation method for estimating time-variant component reliability of vibrating systems, an experimental test procedure, which incorporates the Girsanov transformation step into its folds, has been developed to estimate the time-variant system reliability of engineering systems. The two main ingredients of application of this strategy consists of determination of a control vector, which is artificially introduced to facilitate reduction in sampling variance, and the formulation of the Radon-Nikodym derivative, which serves as the correction to be introduced in order to compensate for the addition of the artificial control. (B) In problems of response analysis of structures subjected to random earthquake loads and vibration of vehicles running on rough roads, it may not be always feasible to completely specify the external actions on the structures. In such situations, it is of interest to determine the most favorable and the least favorable responses, along with the models for missing information in the inputs which produce the extreme responses. The present study, again inspired by existing analytical solutions to this problem, develops an experimental procedure to characterize the optimal excitation models and associated responses. (C) In the context of PsD testing of nonlinear structure to earthquake loads, a refinement in the test procedure involving the treatment of a linearized variational equation is proposed. This has led to the estimation of the evolution of global error norm as test proceeds with time. The estimates of error thus obtained have been used to decide upon altering the time step of integration.