Damage Detection of Structural Systems with Noisy Incomplete Input and Response Measurements

A probabilistic approach for damage detection is presented using noisy incomplete input and response measurements that is an extension of a Bayesian system identification approach developed by the authors. This situation may be encountered, for example, during low-level ambient vibrations when a structure is instrumented with accelerometers that measure the input ground motion and structural response at a few locations but the wind excitation is not measured. A substructuring approach is used for the parameterization of the mass and stiffness distributions. Damage is defined to be a reduction of the substructure stiffness parameters compared with those of the undamaged structure. By using the proposed probabilistic methodology, the probability of various damage levels in each substructure can be calculated based on the available data. A four-story benchmark building subjected to wind and ground shaking is considered in order to demonstrate the proposed approach

Unified probabilistic approach for model updating and damage detection

A probabilistic approach for model updating and damage detection of structural systems is presented using noisy incomplete input and incomplete response measurements. The situation of incomplete input measurements may be encountered, for example, during low-level ambient vibrations when a structure is instrumented with accelerometers that measure the input ground motion and the structural response at a few instrumented locations but where other excitations, e.g., due to wind, are not measured. The method is an extension of a Bayesian system identification approach developed by the authors. A substructuring approach is used for the parameterization of the mass, damping and stiffness distributions. Damage in a substructure is defined as stiffness reduction established through the observation of a reduction in the values of the various substructure stiffness parameters compared with their initial values corresponding to the undamaged structure. By using the proposed probabilistic methodology, the probability of various damage levels in each substructure can be calculated based on the available dynamic data. Examples using a single-degree-of-freedom oscillator and a 15-story building are considered to demonstrate the proposed approach

Model Identification and Seismic Analysis of Meloland Road Overcrossing

This report presents the results of research directed toward model identification and seismic analysis of the MRO. This research has been implemented to meet the requirements of Tasks 4 and 5 of the UNR-D&M research program (Sec. 1.1.3) and also to provide a basis for developing improved bridge modeling procedures as required under the D & M research program on SBOs (Sec. 1.1.4). The scope of this research effort consisted of our development of a finite element model of the MRO whose parameters were estimated through the application of state-of-the-art system identification methods to the MRO's recorded motions from the Imperial Valley Earthquake. These estimated model parameters were also checked for consistency with an overall range of model parameter values computed using established engineering procedures. This model was then used in a series of parametric dynamic analyses of the seismic response of the MRO which enabled us to evaluate the effects of uncertainties in the various model parameters on the demand forces and moments in the structural members and the foundation springs. Maximum foundation spring forces and moments obtained from these analyses were used as input to nonlinear static analyses of the MRO's pile foundations in order to compute the demand forces and moments within the piles. The demand forces and moments within the MRO's structural and pile elements were then compared against the capacities of these elements. These analysis results have been interpreted to assess the seismic performance and design of the MRO, and also to provide an important basis for our development of improved modeling and seismic evaluation procedures for short bridge overcrossing structures. The above efforts have focused on the modeling and analysis of the MRO's translational and rotational response to transverse horizontal input motions; i.e., the bridge's response to vertical and longitudinal input motions was not included in this research. This focus on the MRO's response to transverse horizontal input motions was adopted because: (a) this response will lead to more severe earthquake-induced internal forces and moments, particularly in the central pier which is the element of an SBO that is typically most vulnerable to seismic excitation; and (b) our past evaluations of the MRO's recorded motions have shown that its response to transverse horizontal input motions is strongly affected by SSI, whereas SSI has only a negligible effect of the MRO's response to vertical and longitudinal input motions (Werner, et. al., 1987)

Updating of a Model and its Uncertainties Utilizing Dynamic Test Data

The problem of updating a structural model and its associated uncertainties by utilizing structural response data is addressed. Using a Bayesian probabilistic formulation, 6the updated "posterior" probability distribution of the uncertain parameters is obtained and it is found that for a large number of data points it is very peaked at some "optimal" values of the parameters. These optimal parameters can be obtained by minimizing a positive-definite measure-of-fit function. This paper focuses on the identifiability of the optimal parameters. The problem of finding the whole set of optimal models that have the same output at the observed degrees of freedom for a given input is resolved for the first time, by presenting an algorithm which methodically and efficiently searches the parameter space. Also, a simplified expression is given for the weighting coefficients associated with each optimal model which are involved in the probability distribution for the predicted response

Asymptotic expansions for reliabilities and moments of uncertain dynamic systems

An asymptotic approximation is developed for evaluating the probability integrals which arise in the determination of the reliability and response moments of uncertain dynamic systems subject to stochastic excitation. The method is applicable when the probabilities of failure or response moments conditional on the system parameters are available, and the effect of the uncertainty in the system parameters is to be investigated. In particular, a simple analytical formula for the probability of failure of the system is derived and compared to some existing approximations, including an asymptotic approximation based on SORM methods. Simple analytical formulas are also derived for the sensitivity of the failure probability and response moments to variations in parameters of interest. Conditions for which the proposed asymptotic expansion is expected to be accurate are presented. Since numerical integration is only computationally feasible for investigating the accuracy of the proposed method for a small number of uncertain system parameters, simulation techniques are also used. A simple importance sampling method is shown to converge much more rapidly than straightforward Monte-Carlo simluation. Simple structures subjected to white noise stochastic excitation axe used to illustrate the accuracy of the proposed analytical approximation. Results from the computationally efficient perturbation method are also included for comparison. The results show that the asymptotic method gives acceptable approximations, even for systems with relatively large uncertainty, and in most cases, it outperforms the perturbation method

A Very Efficient Moment Calculation Method for Uncertain Linear Dynamic Systems

The problem of calculating the uncertainty in the dynamic response of a structure due to uncertainties related to the modeling of its dynamic behavior, is addressed. Based on a Bayesian probabilistic approach, a new approximate numerical method is proposed to investigate the resulting uncertainties in the structural response. The proposed method provides a very efficient and accurate approach to the solution of stochastic finite-element models. It can be used to quantify the uncertainties in the predicted response of a structure during its design, where engineering judgement is used to quantify the uncertainties in the modeling process

Probabilistic System Identification and Health Monitoring of Structures

Global health monitoring of a structure is approached by detecting any significant changes in its stiffness distribution through continual updating of a structural model using vibration measurements. A Bayesian probabilistic formulation is used to treat uncertainties which arise from measurement noise, modeling errors, and an inherent nonuniqueness common in this inverse problem