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Model updating of large-scale structures is difficult to carry out when using a frequency response function (FRF) for damage identification, as the solutions for the global system matrices with too many degrees of freedom are required in each iteration. In this paper, a substructure damage identification method is proposed based on the model updating of the acceleration FRF. The original finite element model is divided into several substructures using the improved reduced system (IRS) by the dynamic condensation method, resulting in the simplified substructure model. The final simplified model is composed of the simplified mass matrix and stiffness matrix of the substructure considered. The damage acceleration FRF to be identified is used to iteratively update the simplified model. The locations and extents of the damage elements are obtained by updating the results, which reduces the number of uncertain parameters to be updated and leads to the rapid convergence of the optimization process. In the iteration, L1 norm regularization is introduced to solve the ill-posed problem, which improves the stability of the identification results. A numerical simulation of a six-story steel frame structure under various working conditions was carried out to verify the effectiveness of the proposed method, which was also validated by the experiments. The robustness and performance of the proposed damage identification method based on substructures have been demonstrated.

Time domain substructural condition assessment method is actively researched in recent years to avoid the problem with uncertainties in the different components of the structure, boundary conditions and with an improved effort in the inverse computation. Since the interface force between substructures would vary with the existence of local damages and excitation in the substructures, existing condition assessment method for a full structure cannot be applied directly to the substructures. Also, most existing approaches adopt the state space method in the response prediction. However, the state space method can be shown in this paper inaccurate in the forward substructural dynamic analysis due to the discretization error, and therefore identification based on this method cannot give satisfactory result for a substructure.

The force identification for a full structure based on the explicit Newmark-β method has been shown superior to the state space method [K. Liu et al., J. Sound Vibr.33(3) (2014) 730–744]. This method is extended in this paper for substructural interface force identification. The variation of interface forces between substructures with variation in the substructural condition is illustrated with a plane truss structure. Subsequent condition assessment based on substructural response sensitivity is proposed with the analytical derivation of the sensitivity taking into account the interface force sensitivity which is not small to be ignored. The new damage detection method based on the explicit Newmark-β method and the substructural response sensitivity is verified numerically with different damage scenarios in a plane truss structure giving satisfactory results.

Existing stochastic dynamic response analysis requires the probability distributions of all variables in the system. Some of them are difficult or even impossible to obtain, and assumed probability density functions are often adopted which may lead to potential unrealistic estimation. This error may accumulate with the dimension of the structural system. This paper proposed a strategy to address this problem in the response analysis of a high-dimensional stochastic system. Partial measurement and finite element model of the target substructure of the system are required. The stochastic responses at several unmeasured locations are reconstructed from the measured responses. Only the variability of the substructure is considered. Other parameters outside the substructure are represented by their mean values contributing to the measured responses. The proposed strategy is illustrated with the analysis of a seven-storey plane frame structure using the probability density evolution method integrated with the response reconstruction technique. Measurement noise is noted to have a large influence on stochastic dynamic responses as different from that in a deterministic analysis. The proposed stochastic substructural response analysis strategy is found more computational efficient than traditional approach and with more realistic information of the structure from the measured responses.

Drive-by methods hold tremendous potential for fast inspection and condition evaluation of bridges. However, most literature works focused on the bridge superstructures, and the applications of drive-by approaches to the substructures are quite rare. This paper numerically investigates the feasibility of detecting the damage in high-speed railway (HSR) bridge substructures using measured bogie acceleration responses from the passing marshaling trains. A damage indicator is developed as the work done by the change of the interaction force before and after damage when the vehicle passes through a pier. The interaction forces between the vehicle bogies and wheel-sets are estimated by a dual Kalman filter (DKF) from the dynamic responses of passing vehicles. A rapid inspection methodology is proposed for the interaction force identification and damage detection based on the coupling vehicle-girder-pier-foundation model. Parametric studies are conducted to investigate the influence of some factors on the proposed methodology. The results from this study indicate that the interaction forces and vehicle state can be well identified by the DKF algorithm, and the defined damage indicator is reliable for damage localization and indication of the damage level using vehicles travelling at a high speed. The proposed method shows good robustness to the pier damage combinations, vehicle parameters and track irregularity and can serve as an effective drive-by health monitoring strategy for HSR or even normal speed railway bridge substructures.

The Lambda-Cold Dark Matter (ΛCDM) model describes successfully our Universe on large scales, as has been verified by a wide range of observations. A number of apparent inconsistencies have arisen between observations and ΛCDM predictions on small scales. In this work, the current status of observations on galactic and subgalactic scales is reviewed. Theoretical predictions and recent observations are brought together in order to reveal the nature and severity of the inconsistencies. Lastly, the progress towards the resolution of each one of these conflicts is briefly reviewed.

This paper presents a substructural approach to parameter identification of structures, with the simultaneous identification of structural parameters and input time history of the applied excitation. The substructural approach reduces the computational effort when dealing with large structures. The substructural parameters, including the unknown interface forces at the ends of the substructure, are identified iteratively. The locations of input forces must be known; however, their magnitudes can be unknown. The method requires the measurement of accelerations at the interior DOFs but not interface DOFs of the substructure. Numerical simulations are performed for three examples, viz. global models of a 15 DOF shear building model, a planar truss of 55 members and a cantilever beam of 20 elements. The examples are excited with harmonic, random and impulse excitations. The effect of noisy data is studied. Even with noise, the proposed substructural method is found to identify the structural parameters with appreciable accuracy and with a considerable saving of CPU time. However, the identification of damping parameters is found to be prone to more errors than for the stiffness parameters.

The mutation of mass and stiffness between the superstructure and substructure of a hydropower station can lead to the whiplash effect on the hydropower house during an earthquake. This paper explains the mechanism of the whiplash effect based on the theory of structural dynamics. A Chinese hydropower house was taken as a test case to discuss the whiplash effect on this type of structures. An integral finite element model and partial models of the hydropower house were established according to its structural features, arrangement forms and loading features. The dynamic response and the whiplash effect of the hydropower house were investigated by direct time integration using the Newmark method.

Damage localization is very significant in engineering applications. The existing method based on the chi-square distribution of an autoregressive moving average with exogenous inputs (ARMAX) model residual is not applicable for these realistic excitations except Gaussian excitation. To solve the above problem, this paper presents a structural damage localization method based on the empirical probability mass function (EPMF) of the ARMAX model residual and Kullback–Leibler (KL) divergence. In detail, we employ empirical data analysis (EDA) approach to estimate the EPMF of the ARMAX model residual of the data generated by the arbitrary excitation because EDA does not need any a priori knowledge about the model residual. Moreover, the KL divergence is introduced to measure the dissimilarity of the EPMFs in undamaged and damaged states to prove that our method is effective for arbitrary excitation. Finally, the semi-parametric extreme value theory is used to estimate the reliable threshold for localizing the damage. Numerical simulated and experimental results illustrate that the proposed method localizes the damage under different excitations, respectively.