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Design/optimization of the tuned mass damper (TMD) system may not always lead toward robust performance if uncertainties exist. In view of this, a stochastic design of multiple TMD (MTMD) systems has been proposed in the present study taking into account various uncertainties. Taylor-expansion is used to perturb the objective function facilitating stochastic design/optimization. An interval-extension is used to observe the effect of uncertainties of different levels. The Lyapunov equation is used in the design of TMD systems by minimizing the dispersion of displacement of the primary system. The present work takes into account a model of generalized MTMD system. Seismic excitation is considered as a random process in the form of both: (a) stationary Kanai–Tajimi (KT) filter and (b) stationary Gaussian white noise directly applied to the base of structure. A numerical investigation is carried out to observe the consequences of uncertainties on the optimum design of MTMD parameters for both the excitation models (with and without incorporating Kanai–Tajimi filter). Efficiency of the MTMD systems (with variation of number of MTMD mass-units) is compared under various levels of uncertainties. Finally, some significant earthquake records are utilized toward more realistic understanding on the performance of stochastic design of TMD/MTMD systems under seismic excitation with various levels of uncertainties.

Vibration-based global damage detection based on updating of finite element (FE) model by targeting the modal measurements is a significant area of interest in structural health monitoring (SHM). In a typical modal testing setup, the measured mode shapes have missing components against various degrees of freedom (DOFs) due to the limitation in the number of sensors available. In this context, a novel Gibbs sampling approach is proposed for updating of FE model incorporating model reduction (MR) to facilitate the global-level detection of structural damages from incomplete modal measurements. In addition to the ease with similar sizes of analytical and experimental mode shapes, the proposed Gibbs sampling approach (for updating the reduced order FE model in the Bayesian framework) has some important advantages like: (A) no need for consideration of system mode shapes as parameters (unlike needed in the typical Gibbs sampling approach) thereby having a significant reduction in the number of parameters, (B) non-requirement of mode matching with consequent reduction in computation time to a significant extent. A generalized formulation is presented in this work providing the scope for incorporating measurements from multiple sensor setups. Moreover, formulations are adapted to incorporate multiple sets of data/measurements from each setup targeting the epistemic uncertainty. Finally, validation is carried out with both numerical (truss structure and building structure) and experimental (laboratory building structure) exercises in comparison with the typical Gibbs sampling approach having a full-sized model. The proposed approach is observed to be evolved as a computationally efficient technique with satisfactory performance in FE model updating and global damage detection.

The negative stiffness integrated tuned mass damper (NS-TMD) is considered as an interesting and efficient device for passive vibration control. However, design/optimization of NS-TMD may not always lead towards robust performance if there exist uncertainties. In this study, a stochastic design of NS-TMD is proposed taking into account various types of uncertainties. Taylor-expansion is used to perturb the objective function facilitating a stochastic design/optimization. Besides, an interval-extension is used to observe the effect of uncertainties with different intensities. The Lyapunov equation is used in the proposed design of NS-TMD by minimizing the dispersion of displacement of primary system. The present work takes into account a standard model of NS-TMD in view of wider applicability of the present study. Random vibration is considered in both the cases of: (a) base-excitation and (b) superstructure loading. A numerical investigation is further carried out to observe the consequences of uncertainties on optimum design of NS-TMD parameters for both the cases of base-excitation and superstructure loading. Efficiency of NS-TMD is compared under various levels of uncertainties. Besides, some significant earthquake records and white noise (WN) samples are utilized towards more realistic understanding on the performance of stochastic design of NS-TMD under seismic excitation with different level of uncertainties. NS-TMD appears to be effective in robustness against uncertainties in structural parameters in comparison with the frequently used TMD system. The proposed methodology may be considered as a useful alternative for stochastic design of the NS-TMD under both superstructure loading and base-excitation.

A methodology for probabilistic damage detection in Bayesian framework without any requirement of mode matching is presented with detailed formulations on finite element model updating using incomplete modal data measured using limited number of sensors. Multiple modal measurement/data sets from multiple different sensor set-ups can be used in the proposed methodology with further scope for using repeated measurements from any single sensor set-up. Combined normal–lognormal multivariate distribution is considered in the Bayesian framework. Strictly positive random parameters are assigned with lognormal distribution, while the remaining random parameters are assigned with normal distribution. In this work, the normal distribution is incorporated for the likelihood function, which consists of the eigen-system equation error and the error between the system mode shapes and experimental mode shapes. On the other hand, mass and stiffness parameters are assigned with the lognormal distribution. Detailed formulations for probabilistic identification of changes/damages are also developed. The proposed approach is validated using a three-dimensional building structure considering multiple simulated damage cases. Performance in updating and damage detection is evaluated based on multi-set-up and multi-dataset considerations. Besides, the proposed technique is compared with the similar Bayesian updating solely based on normal distribution and the Gibbs sampling.

This paper presents a novel Gibbs sampling approach for structural health monitoring (SHM) with detection of structural changes/damages using incomplete complex modal data measured with a l...

Sub-structuring of structural system matrices is an important procedure in a typical finite model updating process. The conventional approach of Bayesian model updating is observed to depend on the procedure of sub-structuring of system matrices to a great extent. Without this procedure, detailed formulation for the expression of updated parameters is difficult to obtain in Bayesian framework especially without requirement of mode matching. But sub-structuring is not an easy task to perform in case of complex structures where it is not always easy to write computer program for FE modelling of such structures. Besides, sub-structuring procedure does not yield satisfactory results in case of updating parameters such as geometric properties like depth, width of beam, and beam offset. In order to remove this difficulty, the updated structural parameter in each iteration of linear optimization is obtained using numerical optimization technique where the objective function contains only the structural parameters as variables and last updated values of other updating parameters like system mode shapes as constants. Detailed formulation of the proposed method is carried out along with the estimation of uncertainty and damage detection of model parameters. One numerical example in the form of a three-dimensional steel cantilever beam is considered for demonstration purpose. Computer programs for FE modelling of the cantilever beam is created in MATLAB. Satisfactory performances in updating of model and detection of damage are observed for the structure using the proposed approach.

This study deals with the optimization of parameters of multiple tuned mass damper (MTMD) system for seismic vibration control considering uncertain bounded structural parameters. An approach based on Taylor expansion of objective function along with subsequent interval extension is taken into account in this study. The objective function involving the uncertain bounded parameters is transformed into two independent deterministic sub-problems leading to the lower and upper bound solutions with the help of interval extension. The optimization strategy investigated in this optimization framework is the stochastic structural optimization (SSO) where the root mean square displacement of the primary–secondary coupled system is minimized. A numerical study is performed to observe the effect of uncertainties on the optimization of MTMD parameters where the primary system is coupled with MTMD system with two, three, five and ten mass units. The performance of these MTMD systems is also compared under various levels of uncertainties. Fundamental mode of the system is considered for vibration control, where natural frequency and damping ratio associated with the fundamental mode are found to be nearly 10 rad/s and 0.03, respectively. In this study, natural frequency and damping ratio of the primary system, natural frequency and damping ratio of elastic filter, intensity of the power spectral density of white noise excitation at the bed rock are taken as the uncertain parameters. It is observed that SSO is suitable for higher levels of uncertainties associated with structural parameters. It may be mentioned that such observations are found for various numbers of mass-units of MTMD system.

Finite element (FE) model updating in Bayesian framework, using sampling-based techniques like Markov chain Monte carlo (MCMC), is observed to be investigated by many researchers. The present work is focussed on FE model updating using MCMC techniques where modelling is performed using commercial FE software to avoid the difficulties with writing computer program for FE modelling. In this present work, two prominent MCMC techniques based on Metropolis–Hastings (MH) algorithm, viz. enhanced-MCMC and transitional MCMC are primarily used, while FE modelling is performed using a well-known FE software, viz. SAP2000. A reasonably complex structure in the form of a cantilever plate is considered in this study and modelled using shell elements. Besides, damage is simulated in this plate structure by decreasing the Young’s modulus of few of the elements of the discretized plate structure. Modal data in the form of frequencies and incomplete mode shapes, evaluated from the damaged structure, are taken as the measured modal data. The technique of error localisation and an improved parameter selection method are adopted for limiting the number of updating parameters to facilitate better performance. Moreover, Gibbs sampling which is an effective algorithm of MCMC technique is also demonstrated using SAP2000. All the MCMC techniques for FE model updating are performed using a computational framework based on interactions between MATLAB and SAP2000 with the help of SAP2000 open application programming interface (OAPI). It is observed that level of performances in FE model updating is most satisfactory while using enhanced-MCMC in comparison with others.

Seismic excitations are time varying and spatially varying waveforms depending on the seismotectonics of a region. Analysis of a long structure like bridges, pipelines, dams using uniform seismic excitation is not a realistic approach as the seismic excitation does not remain stationary at every support location. Thus, multi-support seismic excitation is performed to obtain seismic responses of a structure under a realistic situation. In this paper, a replica of a five-span railway bridge (5 spans @ 26.24 m) located in the seismically active north-east zone of India has been studied. A finite element modelling of the total bridge has been created in the SAP2000 software. Synthetic ground motions of moment magnitude (Mw) 8.7 with wave velocity of 1200 m/s have been generated as per the geotechnical and geological conditions of this region considering Oldham and Dauki faults by Stochastic Model Simulation (SMSIM). The synthetic acceleration response has been used for performing nonlinear time-history analysis for both uniform and multi-support seismic excitation study. Nonlinear time-history analysis has been performed to obtain the dynamic response of the total structure due to seismic excitation. The study concludes that the absolute maximum displacement, shear force, bending moment at the total deck and the piers increase in case of multi-support seismic excitation than uniform seismic excitation. This study shows that the codal provisions should incorporate the effect of multi-support excitation and site-specific ground motion details in the design of important structures to keep them operational in extreme hazardous conditions.

Seismic demand can be reduced by modifying the structural response of the system. Viscous dampers are an effective passive control device for reducing vibrations in building structures. The present study investigates the performance of linear viscous dampers in vibration control of multi-storey building structures under seismic excitation considering the effect of soil flexibility. Six-storey steel 3D framed buildings with three different building plans, namely symmetric, T and L shapes, are modeled using SAP 2000. Soil type I (hard) and type II (medium) are considered as per IS 1893:2002 to incorporate the effect of soil flexibility by using springs at supports for medium type soil and fixed supports for hard soil. The spring constants are obtained from Gazetas’ equations. To measure the control performance, inter-storey drift and maximum top displacement are considered as objective functions. Linear time history simulation is performed using white noise (ensuring wider frequency content) to quantify the objective functions. After performing the analysis and comparing with the uncontrolled case for both hard and medium soil, it is observed that maximum reduction in inter-storey drift and average top displacement can be obtained. Eccentric plans have larger uncontrolled values than the symmetric plans, thus additional design criteria to be followed when opting for eccentric plans. The study reveals that application of supplemental viscous dampers results in greater control of vibrations in such plans. Vibration control of viscous damper is comparatively better in hard soil than in medium type soil.

The present work is associated with Bayesian finite element (FE) model updating using modal measurements based on maximizing the posterior probability instead of any sampling based approach. Such Bayesian updating framework usually employs normal distribution in updating of parameters, although normal distribution has usual statistical issues while using non-negative parameters. These issues are proposed to be dealt with incorporating lognormal distribution for non-negative parameters. Detailed formulations are carried out for model updating, uncertainty-estimation and probabilistic detection of changes/damages of structural parameters using combined normal-lognormal probability distribution in this Bayesian framework. Normal and lognormal distributions are considered for eigen-system equation and structural (mass and stiffness) parameters respectively, while these two distributions are jointly considered for likelihood function. Important advantages in FE model updating (e.g. utilization of incomplete measured modal data, non-requirement of mode-matching) are also retained in this combined normal-lognormal distribution based proposed FE model updating approach. For demonstrating the efficiency of this proposed approach, a two dimensional truss structure is considered with multiple damage cases. Satisfactory performances are observed in model updating and subsequent probabilistic estimations, however level of performances are found to be weakened with increasing levels in damage scenario (as usual). Moreover, performances of this proposed FE model updating approach are compared with the typical normal distribution based updating approach for those damage cases demonstrating quite similar level of performances. The proposed approach also demonstrates better computational efficiency (achieving higher accuracy in lesser computation time) in comparison with two prominent Markov Chain Monte Carlo (MCMC) techniques (viz. Metropolis-Hastings algorithm and Gibbs sampling).

The irregularity in the railway tracks is a very common topic of interest among the researchers in recent times. The trains run on the tracks with very high velocities to meet the demands of the passengers. But due to the unevenness of the track, the body of the train car faces vertical accelerations, which in turn causes discomfort to the passengers sitting inside the train car. In the present report, vertical acceleration is analyzed for uneven tracks by taking the car body as a single degree of freedom model. The investigation shows a clear explanation of the critical velocity values for the train, so as to maintain the passenger comfort conditions. Random sinusoidal curves were generated using MATLAB to analyze the random unevenness of the track. It is observed that the vertical accelerations in the car body are directly proportional to the speed of the train. Finally, a critical velocity is proposed for a train running on uneven sinusoidal profile track such that, the vertical acceleration not exceeding 0.2g.

Applications of tuned mass damper (TMD) systems for bridge structures are observed for mitigation of problem related to excessive vibration induced by either wind loading or vehicle loading, where dominant modes usually in one direction (commonly vertical) are taken into account. Considering modes dominant in one direction may not be considered as a robust practice while any bridge structure is having dominant modes along both the transverse and vertical directions and the same bridge structure is subjected to loading along both the directions. In the present study, an approach for simultaneous control of major horizontal, vertical and torsional modes is presented targeting robust vibration control under general loading condition. A strategy using modal frequency response function (FRF) is proposed based on the traditional mode-wise control approach. The proposed modal FRF based approach is applied to an existing important large truss bridge (Saraighat Bridge) to carry out an analytical design of TMD system considering general loading conditions. The designed TMD system is found to demonstrate good performance under various white-noise based general loading conditions.

A Bayesian probabilistic methodology is presented for structural model updating using incomplete measured modal data which also takes into account different types of errors such as modelling errors due to the approximation of actual complex structure, uncertainties introduced by variation in material and geometric properties, measurement errors due to the noises in the signal and the data processing. The present work uses Linear Optimization Problems (LOP) to compute the probability that continually updated the model parameters. A real life rail-cum-roadway long steel truss bridge (Saraighat bridge) is considered in the present study, where identified modal data are available from measured acceleration responses due to ambient vibration. The main contributions of this paper are: (1) the introduction of sufficient number of model parameters at the element property level in order to capture any variations in the sectional properties; (2) the development of an accurate baseline model by utilizing limited sensor data; (3) the implementation of a probabilistic damage detection approach that utilizes updated model parameters from the undamaged state and possibly damaged state of the structure.

Finite element (FE) model updating using measured dynamic data has gained much attention in view of its contribution towards important areas like model-correction, structural health monitoring. Usually model updating is observed to be performed using measured modal data like modal frequencies and mode shapes – indeed very few works are observed to provide scope for using damping measurements in FE model updating. The present work proposes a Bayesian probabilistic FE model updating using multiple sets of complex modal data (viz. complex modal frequencies and complex mode shapes) and thereby enabling the scope for incorporating damping measurements in updating. Moreover there remains the opportunity for using incomplete complex modal data and avoiding the requirement of mode matching. In this paper, a computationally efficient model updating approach based on maximum a posteriori (MAP) is formulated where all the mass, stiffness and damping parameters are updated in a sequential iterative manner. Detailed formulations are obtained considering damping to be contributed by classical damping (Rayleigh damping) and non-classical viscous damping. Besides, formulations for uncertainty estimation and probabilistic damage detection are also developed. The proposed approach is validated using two numerical examples while utilizing incomplete complex modal data. Performance in updating is evaluated for both undamaged and damaged cases. The proposed approach is observed to be successful for updating of FE model as well as for detection of changes/damages in probabilistic manner, while being computationally efficient as well.

A frequency band specific passive control strategy is presented based on H∞ optimization for multi-degree of freedom (MDOF) linear time invariant (LTI) structural systems. Effective control can be achieved if passive control devices are designed by considering frequency bands of excitation. Minimization of maximum spectral norm or worst-case gain in the excitation frequency range is taken into account for the design of passive control devices for effective performance. A multi-storey shear planer frame coupled with a tuned mass damper (TMD) system as the passive control device is considered in the numerical simulation for controlling both displacement and acceleration subjected to base excitation. The band-specific H∞ optimization problem for design of passive control devices has been transformed into GA-friendly form for the TMD system as control devices. Such a design strategy of passive control devices based on minimizing worst-case gain associated to finite frequency band is observed to provide efficient design of a TMD system with better performance than that designed based on conventional H∞ optimization associated to entire frequency range.

A modal approach is considered for sensor placement evaluation in operational modal analysis (OMA) where modal participation at individual degree of freedom (DOF) is evaluated separately for the target modes and subsequently locations are identified using these participation profiles. Modal contribution in output energy (MCOE) is proposed as modal measure to evaluate modal participation and has been applied in this modal approach framework for sensor placement evaluation. MCOE is evaluated using observability grammian for any types of response measurement (displacement, velocity or acceleration), while a system is released from any initial condition. Further, existing modal measures e.g. modal Hankel singular value (MHSV) and system norms (H 2 , H∞ and Hankel) are explained in perspective of OMA. To understand the efficiency of this proposed technique, MCOE is compared in terms of modal participation with existing modal measures as well as with other techniques like effective independence (EI) and modal kinetic energy (MKE). Analytical similarity is found for participation of a mode with EI method. Further, an existing large truss bridge structure is considered for comparative study based on modal participation of individual target modes along each DOF with acceleration measurement. In this comparison, MCOE technique is found to be in very good agreement with EI method as expected, while good agreement is observed with MHSV as well as norms and reasonable agreement with MKE method. Further, the adopted modal approach uses a flexible and insightful methodology for sensor location evaluation for multiple target modes.

There has been an enormous research in the field of seismic performance of structures. The improvement in the performance is still a challenging task for researchers and engineers. Many strategies have been considered in this regard to achieve desirable result. Base isolation is considered to be the most popular method of protecting structures against seismic actions. However, use of different dampers has also been a major revolution in improving the seismic action of buildings. This review article is intended to illustrate different techniques for improving the seismic performance of buildings and bridges. The study mainly emphasizes on the effect of different isolators and dampers in mitigating the damage of buildings and other civil infrastructures. Pertinent study in the review explores the possible application of the devices towards effective utilization in buildings, bridge piers and other structures.

Application of TMD systems are observed for mitigation of excessive vibration of bridge-structures targeting either wind loading or vehicle loading. Usually, dominant modes in one direction (commonly vertical) are taken in account for such passive control using TMD systems. However, considering modes dominant in one direction may not be considered as a robust practice while any bridge structure is having dominant modes along both the transverse and vertical directions and the same bridge structure is subjected to loading along both the directions. An approach for simultaneous control of major horizontal, vertical and torsional modes is presented in the present study targeting robust vibration control under general loading condition. A modal frequency response function (FRF) based strategy is proposed using the traditional mode-wise control approach. The proposed modal FRF based approach is applied to an existing important large truss bridge (Saraighat Bridge) to carry out an analytical design of TMD system considering general loading conditions. A Good control-performance is observed based on this proposed design methodology under various simulated general loading conditions.