Countries world-over have thousands of critical structures and bridges which have been built decades back when strength-based designs were the order of the day. Over the years, magnitude and frequency of loadings on these have increased. Also, these structures have been exposed to environmental degradation during their service life. Hence, structural health monitoring (SHM) has attracted the attention of researchers, world over. Structural health monitoring is recommended both for vulnerable old bridges and structures as well as for new important structures. Structural health monitoring as a principle is derived from condition monitoring of machinery, where the day-to-day recordings of sound and vibration from machinery is compared and sudden changes in their features is reported for inspection and trouble-shooting. With the availability of funds for repair and retrofitting being limited, it has become imperative to rank buildings and bridges that require rehabilitation for prioritization. Visual inspection and expert judgment continues to rule the roost. Non-destructive testing techniques though have come of age and are providing excellent inputs for judgment cannot be carried out indiscriminately. They are best suited for evaluating local damage when restricted areas are investigated in detail. A few modern bridges, particularly long-span bridges have been provided with sophisticated instrumentation for health monitoring. It is necessary to identify local damages existing in normal bridges. The methodology adopted for such identification should be simple, both in terms of investigations involved and the instrumentation. Researchers have proposed various methodologies including damage identification from mode shapes, wavelet-based formulations and optimization-based damage identification and instrumentation schemes and so on. These are technically involved but may be difficult to be applied for all critical bridges, where the sheer volume of number of bridges to be investigated is enormous. Ideally, structural health monitoring has to be carried out in two stages: (a) Stage-1: Remote monitoring of global damage indicators and inference of the health of the structure. Instrumentation for this stage should be less, simple, but at critical locations to capture the global damage in a reasonable sense. (b) Stage -2: If global indicators show deviation beyond a specified threshold, then a detailed and localized instrumentation and monitoring, with controlled application of static and dynamic loads is to be carried out to infer the health of the structure and take a decision on the repair and retrofit strategies. The thesis proposes the first stage structural health monitoring methodology using natural frequencies and static deflections as damage indicators. The idea is that the stage-1 monitoring has to be done for a large number of bridges and vulnerable structures in a remote and wire-less way and a centralized control and processing unit should be able to number-crunch the in-coming data automatically and the features extracted from the data should help in determining whether any particular bridge warrants second stage detailed investigation. Hence, simple and robust strategies are required for estimating the health of the structure using some of the globally available response data. Identification methodology developed in this thesis is applicable to distributed smeared damage, which is typical of reinforced concrete structures. Simplified expressions and methodologies are proposed in the thesis and numerically and experimentally validated towards damage estimation of typical structures and elements from measured natural frequencies and static deflections. The first-order perturbation equation for a dynamical system is used to derive the relevant expressions for damage identification. The sensitivity of Eigen-value-cumvector pair to damage, modeled as reduction in flexural rigidity (EI for beams, AE for axial rods and Et 12(1 2 )3− μ for plates) is derived. The forward equation relating the changes in EI to changes in frequencies is derived for typical structural elements like simply-supported beams, plates and axial rods (along with position and extent of damage as the other controlling parameters). A distributed damage is uniquely defined with its position, extent and magnitude of EI reduction. A methodology is proposed for the inverse problem, making use of the linear relationship between the reductions in EI (in a smeared sense) to Eigen-values, such that multiple damages could be estimated using changes in natural frequencies. The methodology is applied to beams, plates and axial rods. The performance of this inverse methodology under influence of measurement errors is investigated for typical error profiles. For a discrete three dimensional structure, computationally derived sensitivity matrix is used to solve the damages in each floor levels, simulating the post-earthquake damage scenario. An artificial neural network (ANN) based Radial basis function network (RBFN) is also used to solve the multivariate interpolation problem, with appropriate training sets involving a number of pairs of damage and Eigen-value-change vectors. The acclaimed Cawley-Adams criteria (1979) states that, “the ratio of changes in natural frequencies between two modes is independent of the damage magnitude” and is governed only by the position (or location) and extent of damage. This criterion is applied to a multiple damage problem and contours with equal frequency change ratios, termed as Iso_Eigen_value_change contours are developed. Intersection of these contours for different pairs of frequencies shows the position and extent of damage. Experimental and analytical verification of damage identification methodology using Cawley-Adams criteria is successfully demonstrated. Sensitivity expressions relating the damages to changes in static deflections are derived and numerically and experimentally proved. It is seen that this process of damage identification from static deflections is prone to more errors if not cautiously exercised. Engineering and physics based intuition is adopted in setting the guidelines for efficient damage detection using static deflections. In lines of Cawley-Adams criteria for frequencies, an invariant factor based on static deflections measured at pairs of symmetrical points on a simply supported beam is developed and established. The power of the factor is such that it is governed only by the position of damage and invariant with reference to extent and magnitude of damage. Such a revelation is one step ahead of Caddemi and Morassi’s (2007) recent paper, dealing with static deflection based damage identification for concentrated damage. The invariant factor makes it an ideal candidate for base-line-free measurement, if the quality and resolution of instrumentation is good. A moving damage problem is innovatively introduced in the experiment. An attempt is made to examine wave-propagation techniques for damage identification and a guideline for modeling wave propagation as a transient dynamic problem is done. The reflected-wave response velocity (peak particle velocity) as a ratio of incident wave response is proposed as a damage indicator for an axial rod (representing an end-supported pile foundation). Suitable modifications are incorporated in the classical expressions to correct for damping and partial-enveloping of advancing wave in the damage zone. The experimental results on axial dynamic response of free-free beams suggest that vibration frequency based damage identification is a viable complementary tool to wave propagation. Wavelet-multi-resolution analysis as a feature extraction tool for damage identification is also investigated and structural slope (rotation) and curvatures are found to be the better indicators of damage coupled with wavelet analysis. An adaptive excitation scheme for maximizing the curvature at any arbitrary point of interest is also proposed. However more work is to be done to establish the efficiency of wavelets on experimentally derived parameters, where large noise-ingression may affect the analysis. The application of time-period based damage identification methodology for post-seismic damage estimation is investigated. Seismic damage is postulated by an index based on its plastic displacement excursion and the cumulative energy dissipated. Damage index is a convenient tool for decision making on immediate-occupancy, life-safety after repair and demolition of the structure. Damage sensitive soft storey structure and a weak story structure are used in the non-linear dynamic analysis and the DiPasquale-Cakmak (1987) damage index is calibrated with Park-Ang (1985) damage index. The exponent of the time-period ratio of DiPasquale-Cakmak model is modified to have consistency of damage index with Park-Ang (1985) model.

Uncertainties are present in the inverse analysis of damage identification with respect to the given measurements, mainly the modelling uncertainties and the measurement uncertainties. Modelling uncertainties occur due to constructing a representative model of the real structure through finite element modelling, and representing damage in the real structures through changes in material parameters of the finite element model (assuming smeared crack approach). Measurement uncertainties are always present in the measurements despite the accuracy with which the measurements are measured or the precision of the instruments used for the measurement. The modelling errors in the finite element model are assumed to be encompassed in the updated uncertain parameters of the finite element model, given the uncertainties in the measurements and in the prior uncertainties of the parameters. The uncertainties in the direct measurement data are propagated to the estimated output data. Empirical models from codal provisions and standard recommendations are normally used for prediction of long-time deformations in concrete structures. Uncertainties are also present in the creep and shrinkage models, in the parameters of these models, in the shrinkage and creep mechanisms, in the environmental conditions, and in the in-situ measurements. All these uncertainties are needed to be considered in the damage identification and prediction of long-time deformations in concrete structures. In the context of modelling uncertainty, uncertainties can be categorized into aleatory or epistemic uncertainty. Aleatory uncertainty deals with the irresolvable indeterminacy about how the uncertain variable will evolve over time, whereas epistemic uncertainty deals with lack of knowledge. In the field of damage detection and prediction of long time deformations, aleatory uncertainty is modeled through probabilistic analysis, whereas epistemic uncertainty can be modeled through (1) Interval analysis (2) Ellipsoidal modeling (3) Fuzzy analysis (4) Dempster-Shafer evidence theory or (5) Imprecise probability. Many a times it is di cult to determine whether a particular uncertainty is to be considered as an aleatory or as an epistemic uncertainty, and the model builder makes the distinction. The model builder makes the choice based on the general state of scientific knowledge, on the practical need for limiting the model sophistication to a significant engineering importance, and on the errors associated with the measurements. Measurement uncertainty can be stated as the dispersion of real data resulting from systematic error (instrumental error, environmental error, observational error, human error, drift in measurement, measurement of wrong quantity) and random error (all errors apart from systematic errors). Most of instrumental errors given by the manufacturers are in terms of plus minus ranges and can be better represented through interval bounds. The vagueness involved in the representation of human error, observational error, and drift in measurement can be represented through interval bounds. Deliberate measurement of wrong quantity through cheaper and more convenient measurement units can lead to bad quality data. Quality of data can be better handled through interval analysis, with good quality data having narrow width of interval bounds and bad quality data having wide interval bounds. The environmental error, the electronic noise coming from transmitting the data and the random errors can be represented through probability distribution functions. A major part of the measurement uncertainties is better represented through interval bounds and the other part, is better represented through probability distributions. The uncertainties in the direct measurement data are propagated to the estimated output data (in damage identification techniques, the damaged parameters, and in the long-time deformation, the uncertain parameters of the deformation models, which are then used for the prediction of long-time deformations). Uncertainty based damage identification techniques and long-time deformations in concrete structures require further studies, when the measurement uncertainties are expressed through interval bounds only, or through both interval and probability using imprecise techniques. The thesis is divided into six chapters. Chapter 1 provides a review of existing literature on uncertainty based techniques for damage identification and prediction of long-time deformations in concrete structures. A brief review of uncertainty based methods for engineering applications is made, with special highlight to the need of interval analysis and imprecise probability for modeling uncertainties in the damage identification techniques. The review identifies that the available techniques for damage identification, where the uncertainties in the measurements and in the structural and material parameters are expressed in terms of interval bounds, lack e ciency, when the size of the damaged parameter vector is large. Studies on estimating the uncertainties in the damage parameters when the uncertainties in the measurements are expressed through imprecise probability analysis, are also identified as problems that will be considered in this thesis. Also the need for estimating the short-term time period, which in turn helps in accurate prediction of long-time deformations in concrete structures, along with a cost effective and easy to use system of measuring the existing prestress forces at various time instances in the short-time period is noted. The review identifies that most of modelers and analysts have been inclined to select a single simulation model for the long-time deformations resulted from creep, shrinkage and relaxation, rather than take all the possibilities into consideration, where the model selection is made based on the hardly realistic assumption that we can certainly select a correct, and the lack of confidence associated with model selection brings about the uncertainty that resides in a given model set. The need for a single best model out of all the available deformation models is needed to be developed, when uncertainties are present in the models, in the measurements and in the parameters of each models is also identified as a problem that will be considered in this thesis. In Chapter 2, an algorithm is proposed adapting the existing modified Metropolis Hastings algorithm for estimating the posterior probability of the damage indices as well as the posterior probability of the bounds of the interval parameters, when the measurements are given in terms of interval bounds. A damage index is defined for each element of the finite element model considering the parameters of each element are intervals. Methods are developed for evaluating response bounds in the finite element software ABAQUS, when the parameters of the finite element model are intervals. Illustrative examples include reinforced concrete beams with three damage scenarios mainly (i) loss of stiffness, (ii) loss of mass, and (iii) loss of bond between concrete and reinforcement steel, that have been tested in our laboratory. Comparison of the prediction from the proposed method with those obtained from Bayesian analysis and interval optimization technique show improved accuracy and computational efficiency, in addition to better representation of measurement uncertainties through interval bounds. Imprecise probability based methods are developed in Chapter 3, for damage identifi cation using finite element model updating in concrete structures, when the uncertainties in the measurements and parameters are imprecisely defined. Bayesian analysis using Metropolis Hastings algorithm for parameter estimation is generalized to incorporate the imprecision present in the prior distribution, in the likelihood function, and in the measured responses. Three different cases are considered (i) imprecision is present in the prior distribution and in the measurements only, (ii) imprecision is present in the parameters of the finite element model and in the measurement only, and (iii) imprecision is present in the prior distribution, in the parameters of the finite element model, and in the measurements. Illustrative examples include reinforced concrete beams and prestressed concrete beams tested in our laboratory. In Chapter 4, a steel frame is designed to measure the existing prestressing force in the concrete beams and slabs when embedded inside the concrete members. The steel frame is designed to work on the principles of a vibrating wire strain gauge and is referred to as a vibrating beam strain gauge (VBSG). The existing strain in the VBSG is evaluated using both frequency data on the stretched member and static strain corresponding to a fixed static load, measured using electrical strain gauges. The crack reopening load method is used to compute the existing prestressing force in the concrete members and is then compared with the existing prestressing force obtained from the VBSG at that section. Digital image correlation based surface deformation and change in neutral axis monitored by putting electrical strain gauges across the cross section, are used to compute the crack reopening load accurately. Long-time deformations in concrete structures are estimated in Chapter 5, using short-time measurements of deformation responses when uncertainties are present in the measurements, in the deformation models and in the parameters of the deformation models. The short-time period is defined as the least time up to which if measurements are made available, the measurements will be enough for estimating the parameters of the deformation models in predicting the long time deformations. The short-time period is evaluated using stochastic simulations where all the parameters of the deformation models are defined as random variables. The existing deformation models are empirical in nature and are developed based on an arbitrary selection of experimental data sets among all the available data sets, and each model contains some information about the deformation patterns in concrete structures. Uncertainty based model averaging is performed for obtaining the single best model for predicting the long-time deformation in concrete structures. Three types of uncertainty models are considered namely, probability models, interval models and imprecise probability models. Illustrative examples consider experiments in the Northwestern University database available in the literature and prestressed concrete beams and slabs cast in our laboratory for prediction of long-time prestress losses. A summary of contributions made in this thesis, together with a few suggestions for future research, are presented in Chapter 6. Finally the references that were studies are listed.