X. Y. Li

Damage Identification of Structures Including System Uncertainties and Measurement Noise

This paper proposes a statistical method for the damage identification of structures based on the measured acceleration response with reference to an analytical model. Uncertainties in the system parameters, such as the structural parameters of the finite element model, the excitation force acting on the structure, and the measured acceleration response from the perturbed state of the structure, are discussed and they are included in the study of the damage identification. Each of these uncertainties is assumed to have a zero mean and is normally distributed. The propagation of each of these uncertainties in an updating damage-identification algorithm is then studied, based on the response-sensitivity approach. A three-dimensional, five-bay, steel-frame structure with local damage in two members is studied for illustration. The mean and standard deviations of the local stiffness parameters identified compare favorably with those from the Monte Carlo technique. The probability density function of the identified local stiffness parameters in both the intact and perturbed states is compared in a subsequent reliability assessment.

Condition Assessment of Structures Under Ambient White Noise Excitation

This paper proposes a damage detection method based on the wavelet packet energy of covariance of measured acceleration responses of structures under ambient excitation. It is a model-based method comparing the measured acceleration responses before and after damage occurrence. The ambient excitation is assumed to be white noise. A damage index based on the change of modal strain energy is used for damage localization. The damage quantification is performed using the sensitivity of the wavelet packet energy of the covariance function. A cantilever five-bay truss structure is used to demonstrate the efficiency of the method with three damage scenarios. The combined two-stage approach is shown capable of locating and accurately quantifying local damages in the presence of measurement noise. A nine-bay three-dimensional truss structure is also assessed in the laboratory with the proposed method, and the whole process of damage detection with incomplete and noisy measurement, initial model error, etc., is demonstrated to be successful for identifying, with good accuracy, local damages in members.

Structural Condition Assessment from White Noise Excitation and Covariance of Covariance Matrix

The sensitivity of covariance of covariancematrix with respect to a local stiffness change in the structural system is derived analytically based on the auto/cross-correlation function of the acceleration response, and the original covariance of covariance formula is improved for use with any number of selected structure modes. This paper presents the approach using the improved covariance of covariance matrix of acceleration response for structural condition assessment under white noise support excitation. A simply supported 31 bar plane truss with and without 10% measurement noise is studied numerically. Results show that the sensitivity approach with the covariance of covariance matrix is accurate, and when including the finite impulse response forward and backward filtering technique, themethod would be suitable for industrial application. The covariance of covariancemethod is shown to be insensitive to measurement noise when the measurement time duration is sufficiently long.

Consistent Regularization for Damage Detection with Noise and Model Errors

NUMBER of methods have been developed for damage detection in the last two decades. Many of the methods are based on the observation of dynamic behavior of a structure (Doebling et al. [1], Brincker et al. [2], Maeck and DeRoeck [3]), among which the sensitivity approach via a model-updating technique is commonly accepted and applied extensively in the engineering industry because of its clear mathematical background andquantitativeindications.However,thistypeofmethodisweakat accommodating the influence of measurement errors, leading to illconditioned problems, as demonstrated by Friswell et al. [4] and Humar et al. [5]. This shortcoming means that the existence and uniqueness of the solution is not ensured and numerical instability is likely to take place in the course of the solution process [6,7]. Investigations have since been conducted to deal with the illconditioned problems in model updating. Hansen [8,9] and Vogel [10] proposed regularization methods for obtaining a solution of the inverse problem. It is recognized in regularization theory that the conventional output error, which is usually the vector of differences between thecomputedandmeasuredresponses,canbemadeunrealistically small if the process of damage identification is allowed to behave badly, such that the variable has arbitrarily large deviations from the true set of parameter change, or there may be infinite sets of ill-posed solutions. A stable solution scheme can be achieved by imposing certain constraints in the form of added penalty terms with adjustable weighting parameters based on posterior knowledge. Recently,TiturusandFriswell[11]presentedthesensitivity-based model-updating method with an additional regularization criterion and computed the solutions based on the generalized singular value decomposition.Specificfeaturesoftheparameterandresponsepaths were explored when the regularization parameter varies. The four different types of spaces that arise in the solution were discussed, together with the characteristics of the families of the regularized solution. Weber et al. [12] applied the Tikhonov regularization and truncated singular value decomposition consistently to a nonlinear updating problem. Line-search and stopping criteria known from numericaloptimizationwereadaptedtotheregularizedproblem.The optimal regularization parameter was determined by generalized cross-validation. From experiences gained in model updating with laboratory test structures, the authors found that Tikhonov regularization can give the optimal solution when there is no noise or very small noise in the measurement. But in the updating procedure for a nonlinear inverse problem with the inclusion of noise and model error, the signal-tonoise ratio is getting smaller [13,14] with each iteration, and the solution obtained from a poor regularization parameter is usually unacceptable. The algorithm does not accurately converge, and the results depend strongly on the convergence criteria and tolerances. In this paper, two techniques are proposed in a new regularization method for the identification of local damages in a structure. One technique proposed a new side condition that classified the elements aspossiblydamagedandundamagedelements,whichwillbetreated differently later. The other technique restricts the range of variation of the regularization parameter, such that the regularization solution will be in a realistic range, and the correct optimal point from the curvature of the L-curve is consistently chosen to ensure a continuousconvergingprocess.Bothtechniquesmakefulluseofthe information from results obtained in previous iteration steps. A plane frame structure is studied with two damaged elements and different levels of noise and model errors to illustrate the application of the proposed method. Numerical results show that the proposed consistent regularization method is very effective at improving the results in the inverse problem with ill-conditioning, compared with the conventional Tikhonov regularization.

Long-Term Health Monitoring of In-service Bridge Deck by Covariance of Covariance Matrix of Acceleration Responses

The covariance of covariance (CoC) matrix is formed from the auto/cross-correlation function of acceleration responses of a structure under white noise ambient excitation. The components are function of the modal parameters of the structure and contain more information on the vibration modes of the structure compared to the general existing methods for extracting the modal parameters. This paper makes use of the CoC matrix and a new pattern match criterion for long-term health monitoring, damage localization and quantification of a five-bay three-dimensional frame structure. A large amount of measured data from an in-service suspension bridge is also analyzed. Only the acceleration responses are required to compute the covariance of covariance matrix. The components of the matrix are analyzed and the effects of the traffic flow and environmental temperature are studied. Finally, a strategy to identify the abnormal state of the bridge is presented based on the properties of the CoC components of the bridge. The CoC matrix is shown suitable for analyzing huge amount of measured data for the output-only structural damage detection without need of an analytical model.

Damage Detection for Structures under Ambient Vibration via Covariance of Covariance Matrix and Consistent Regularization

A consistent regularization technique is adopted for the inverse identification of local damages in a structure under ambient vibration. The consistent regularization method fully makes use of the information from results obtained in previous iteration steps. Some elements are identified as undamaged and others are updated with small incremental steps between iterations. The covariance of covariance matrix which are formed from the auto/cross-correlation function of acceleration responses of a structure under white noise ambient excitation are used for damage detection in this paper. The components of the covariance matrix are proved to be function of the modal parameters (modal frequency, mode shape and damping parameter) of the structure. The number of vibration modes of the structure associated with the components is only limited by the sampling frequency. A simply supported thirty-one bar plane truss structure and a seven-floor frame structure are studied where a multiple damage scenario with different noise levels are identified. Numerical results show that the consistent regularization method combined with covariance of covariance matrix is very effective in improving the results in the inverse problem with ill-condition phenomenon compared with the Tikhonov regularization.

Reliability Analysis of Composite Laminate Structures by Moving Kriging Interpolation Response Surface Method

A response surface method (RSM) for composite laminate structures is proposed in this paper, which is based on the moving Kriging interpolation. The substitute limit state function for failure criteria is discussed and constructed on series of deterministic finite element analysis. Combined with first order reliability method, reliabilities of composite laminate structures are subsequently obtained. Reliability analysis of a composite laminate plate, as a numerical example, is illustrated by the proposed method. The results demonstrate the practicability of the method.

Strong Motion Records of Two Suspension Bridges in a M4.8 Earthquake

Earthquake records of in-service, long-span bridges provide valuable insights into their seismic behavior and performance. In this paper, the strong motion records of arrays installed at two steel suspension bridges in a M4.8 earthquake are illustrated and preliminarily analyzed. The data reveal that the differences in the arrival times of peaks and valleys appear to be significant, which clearly illustrates the wave propagation effect. It is also shown that the differences in local soil conditions at different towers have significant influence on the spectra and time history of ground motions. The results suggest that the spatial variation of seismic ground motions induced by local site effect should receive more attention in seismic design and analysis of long-span bridges.

Health Monitoring of in-Service Bridge Deck by Covariance of Covariance Matrix of Acceleration

A new matrix on the covariance of covariance is formed from the auto/cross-correlation function of acceleration responses of a structure under white noise ambient excitation. The components of the covariance matrix are proved to be function of the modal parameters (modal frequency, mode shape and modal damping) of the structure. The number of vibration modes associated with components of the matrix is only limited by the sampling frequency. Compared to the general methods for extracting modal parameters, the formulated covariance matrix contains more information on the vibration modes of the structure. An in-service suspension bridge is analyzed. Only the output acceleration responses are used to compute the covariance of covariance (CoC) matrix and the Pattern Assurance Criterion (PAC) values. From the CoCs variation and the changing trend of the PAC curve, the healthy condition of the bridge is assessed. The method is independent of analytical model and huge amount of data can be analyzed. It is especially suitable for long-term on-line health monitoring of a structure.