Random Seismic Excitation Research Articles

Stochastic design optimization of nonlinear structures under random seismic excitations using incremental dynamic analysis

Stochastic design optimization of nonlinear structures under random seismic excitations using incremental dynamic analysis

Seismic vulnerability analysis of a high‐rise steel frame structure equipped with novel displacement‐amplified viscoelastic dampers

SummaryThe energy dissipation capacity of conventional viscoelastic dampers (VEDs) cannot be fully exerted due to the relatively small inter‐story displacement of building structures. Thus, a novel VED with a displacement amplification mechanism based on the lever principle is developed in this study to achieve small displacement but high energy dissipation ability. First, the structural layout of an amplified viscoelastic damper (AVED) system is briefly introduced, and then the displacement amplification effect is described in detail. According to the working principle of the AVED and the relationship of force and geometric displacement in an actual frame structure, the restoring force theoretical formula of the corresponding amplified damper is derived. Based on the restoring force of the AVED and in combination with the secondary development function of the ABAQUS unit, a VUEL subroutine suitable for the explicit algorithm is programmed with the FORTRAN language. Then, the correctness of the subroutine is verified through a comparative analysis of the ABAQUS simulation and theoretically calculated results. Consequently, the vulnerability analysis of a high‐rise steel frame structure is conducted by using the incremental dynamic analysis (IDA) method, and the influence of the AVED on the seismic performance of the steel frame structure is quantitatively analyzed from the perspective of probability statistics. The analysis results show that compared with the VED structure, the failure probability of the AVED‐2 and AVED‐3 structures reaching the ultimate failure state at all levels is reduced by approximately 43% and 57%, respectively, and the collapse margin ratio (CMR) of structures under large earthquakes is increased by approximately 35% and 68%, respectively. This indicates that the AVED structures with displacement‐amplified dampers have a better effect on the seismic stability of tall steel frame structures under random seismic excitations. This study aims to provide comprehensive information for the seismic‐resistant design of tall buildings in earthquake‐prone regions.

An iterative gradient descent-based reinforcement learning policy for active control of structural vibrations

A contemporary policy gradient-based optimization scheme is presented for active structural control by exerting the concept of reinforcement learning (RL). The RL-based control algorithm is demonstrated both in proportional (P) state, and proportional-integral (PI) state-output feedback approaches, wherein, the latter strategy is deliberated based on the theory of servo-mechanism. The search for optimal P and PI controller parameters in a training sequence is attained by engaging an efficient gradient descent-based optimization strategy. The utilization of gradient-based sequence within the RL framework accelerates the learning protocol, ensuring effective dissipation of structural energy, and achieving suboptimal control. The proposed algorithms are validated through numerical experiments on two different structural systems: (i) a quarter car model subjected to periodic road excitation, having a single actuator and presented in continuous time, and (ii) an 8-story building model subjected to random seismic excitation, having multiple actuators and presented in discrete time. Practical implementation concerns of control strategies are thoroughly investigated by considering perturbations in model parameters and input forces. The findings from this study indicate that the RL-based P and PI controllers exhibit high stabilizing performance, and are applicable in both analog and digital domains. Finally, it has affirmed that the proposed RL algorithms exhibit relatively low computational complexity in real-time, and thus, open up a wide range of perspectives for its application in large-scale complex structures.

Optimal design of SMA damper for vibration control of connected building under random seismic excitation

To alleviate the earthquake induced damages in closely spaced high-rise buildings, linear or non-linear dampers have been frequently employed. Out of different options, the frequently utilized non-linear damper is the yield damper. Yield damper shows good floor displacement control efficiency, but increases peak floor acceleration and leaves large residual deformation at the end of ground motion. Also, it shows degradation in the hysteresis loop; whereas to achieve a good acceleration and displacement control efficiency, it is imperative to have a stable hysteresis loop with negligible residual deformation. In this context, shape memory alloy (SMA) composed damper has been viewed as a potential solution to reduce floor displacement and acceleration, simultaneously. Also, it offers excellent recentering property and good seismic energy dissipation capacity. This research aims to use the above stated superior properties of SMA and investigate the seismic response control efficiency of optimally design SMA damper for connected buildings, and compare with the yield damper. Optimal stochastic responses of connected buildings are estimated under random earthquake, as modeled using the Kanai-Tajimi power spectra. To linearize the non-linear force–displacement behavior of SMA and yield damper, a statistical linearization approach is adopted. The RMS (root mean square) floor acceleration and RMS floor displacement ratios are determined as response outputs for the damper connected buildings. Studies results show that, optimally designed SMA damper is more effective in reducing acceleration of stiff building and displacement of the flexible building than the yield damper. Compared to the yield damper, SMA damper reduces the RMS acceleration ratios by 15 % for the flexible building and 35 % for the stiff building; and RMS displacement by 20 % for the flexible building and 0.5 % for the stiff building. Overall, SMA damper provide much better seismic response control efficiency for connected buildings than yield damper.

Neural network-based reduced-order modeling for nonlinear vertical sloshing with experimental validation

In this paper, a nonlinear reduced-order model based on neural networks is introduced in order to model vertical sloshing in presence of Rayleigh–Taylor instability of the free surface for use in fluid–structure interaction simulations. A box partially filled with water, representative of a wing tank, is first set on vertical harmonic motion via a controlled electrodynamic shaker. Accelerometers and load cells at the interface between the tank and an electrodynamic shaker are employed to train a neural network-based reduced-order model for vertical sloshing. The model is then investigated for its capacity to consistently simulate the amount of dissipation associated with vertical sloshing under different fluid dynamics regimes. The identified tank is then experimentally attached at the free end of a cantilever beam to test the effectiveness of the neural network in predicting the sloshing forces when coupled with the overall structure. The experimental free response and random seismic excitation responses are then compared with that obtained by simulating an equivalent virtual model in which the identified nonlinear reduced-order model is integrated to account for the effects of violent vertical sloshing.

Seismic reliability research of continuous girder bridge considering fault-tolerant semi-active control

Continuous girder bridge is one of the most widely used bridge types at present, but its structural characteristics are not conducive to earthquake resistance. Therefore, it is of great practical significance to study the damping control of continuous girder bridges. Considering that the control device may fail due to external factors, this paper uses the magnetorheological damper as the damping device to carry out the research on the damping control of the large-span continuous girder bridge. The traditional damping control scheme is improved, and a semi-active control scheme considering fault-tolerance is proposed. That is, when some dampers fail, the fault-tolerant control algorithm provides compensation output to the control system. The seismic response and damping rate of bridges under different control schemes are compared and analyzed, and the seismic reliability of structures under different control schemes and different threshold conditions under random seismic excitation is obtained based on probability density evolution method and random ground motion model. It is found that the semi-active control scheme considering fault tolerance can still make the continuous girder bridge achieve the expected control effect when the control system has faults.

Sliding Mode Control for Semi-Active Damping of Vibrations Using on/off Viscous Structural Nodes

Structural vibrations have adverse effects and can lead to catastrophic failures. Among various methods for mitigation of vibrations, the semi-active control approaches have the advantage of not requiring a large external power supply. In this paper, we propose and test a sliding mode control method for the semi-active mitigation of vibrations in frame structures. The control forces are generated in a purely dissipative manner by means of on/off type actuators that take the form of controllable structural nodes. These nodes are essentially lockable hinges, modeled as viscous dampers, which are capable of the on/off control of the transmission of bending moments between the adjacent beams. The control aim is formulated in terms of the displacement of a selected degree of freedom. A numerically effective model of such a node is developed, and the proposed control method is verified in a numerical experiment of a four-story shear structure subjected to repeated random seismic excitations. In terms of the root-mean-square displacement, the control reduced the response by 48.4–78.4% on average, depending on the number and placement of the applied actuators. The peak mean amplitude at the first mode of natural vibrations was reduced by as much as 70.6–96.5%. Such efficiency levels confirm that the proposed control method can effectively mitigate vibrations in frame structures.

Responses of SDOF Structures With SPIS-<b>Ⅱ</b> Dampers Under Random Seismic Excitation

A closed-form solution of response of SDOF structure with SPIS-II damper subjected to seismic excitation modeled by Clough-Pezien spectrum is proposed, and the shock absorption performance and influencing factors of that system are studied based on the proposed method. Firstly, the equation of motion of SPIS-II damper is established, and the unified expression of the structural response frequency domain solution such as structural displacement and inertial output force are obtained. Secondly, based on the rational expression decomposition and residue theorem, quadratic quadrature equations of frequency response eigenvalue function and Clough-Pezien spectrum are obtained respectively, and then quadratic quadrature equations of structural response power spectrum are induced. Thirdly, concise closed-form solutions of the 0 ~ 2 order spectral moments of the structural response are acquired. The proposed method and the virtual excitation method are used to analyze a case respectively, which verifies the correctness of the proposed method. Finally, the proposed method is used to analyze the influence of the parameters of inertia capacity on the seismic performance of the structure. The research shows that the response solution obtained by the method in this paper is a closed-form solution, which is better than the virtual excitation method in terms of computational efficiency and computational accuracy; when <i>μ</i>_<i>ω</i>unchanged, the damping performance is enhanced with the increasing of <i>μ</i>_<i>m</i>and <i>μ</i>_<i>ξ</i>; when <i>μ</i>_<i>ω</i>=1, the damping performance is improved to the greatest.

Influence of uncertainty of structural parameters on the stochastic dynamic response of asphaltic lining dam-foundation systems to non-stationary random seismic excitation

The present work aims toward the effect of uncertain structural parameters on the stochastic dynamic response of an asphaltic lining dam-foundation system subjected to stationary as well as non-stationary random excitation. Uncertain structural parameters of interest are shear modulus and mass density, modeled using the lognormal distribution. The stochastic seismic response of the dam-foundation system to the random loads with uncertain structural parameters is carried out with the Monte Carlo simulation method. The spatial variability of ground motion is considered with incoherence and wave passage effects as stationary as well as non-stationary random excitation. A time-dependent frequency response function is used throughout the study for non-stationary responses. Obtained results indicate that the variability of shear modulus and mass density can be neglected in stochastic dynamic analysis of an asphaltic lining dam-foundation system. Also, it is seen from the results that stationarity is a reasonable assumption for asphaltic lining dams to typical durations of strong shaking.

Topology optimization of non-linear viscous dampers for energy-dissipating structures subjected to non-stationary random seismic excitation

Topology optimization of non-linear viscous dampers for energy-dissipating structures subjected to non-stationary random seismic excitation

Seismic Fragility of a Multi-Frame Box-Girder Bridge Influenced by Seismic Excitation Angles and Column Height Layouts

Curved multi-frame box-girder bridges with hinges are widely used in the United States due to the large spanning capacity, construction simplification and construction cost economy. This type of bridge frequently has the characteristics of column height asymmetry, adjacent bridge frames vibrating discrepancy. The combination of curved shape and random seismic excitation angles could aggravate the irregularity of the structural seismic response. In this study, an OpenSees model is established for an example bridge, and the hinge is taken as a key component to observe. The impacts of seismic excitation angles and column height layouts on fragility are investigated through the comparison of the fragility curves. The conclusions list the most unfavorable seismic excitation angles corresponding to the fragilities of bridge system, plug-type concrete elements in hinges, hinge restrainers, columns, abutment bearings as well as the secondary components, respectively. The symmetrical column height layout is proved to be beneficial to mitigate the damage risks of restrainers in intermediate hinges and reduce the fragility of the bridge system. This study can provide a reference for the rapid assessment of the fragile position and damage degree of bridges through structural configuration and shape, as well as the seismic excitation angle.

Adaptive Hermite Distribution Model with Probability-Weighted Moments for Seismic Reliability Analysis of Nonlinear Structures

In this paper, an adaptive Hermite distribution model with probability-weighted moments (PWMs) is proposed for evaluating the extreme-value distribution (EVD) of response, which serves as the basis of seismic reliability analysis of complex nonlinear structures under random seismic excitations. From the perspective of EVD, the problem formulation is first introduced. Then, an adaptive distribution model, named as the adaptive Hermite polynomial normal transformation model (A-HPNT), is established to estimate the EVD. The undetermined coefficients of A-HPNT are specified via the PWMs matching technique, in which only linear systems of equations need to be solved. To optimally determine the degree for A-HPNT, a two-step criterion is effectively established accordingly. An efficient high-dimensional sampling technique is introduced for generating samples of extreme value, estimating both the PWMs and statistical moments of EVD. When the entire distribution of EVD is recovered, one can compute the failure probability and reliability index via an integral over the EVD. Two numerical examples, a 10-story nonlinear shear frame structure and a practical 13-story reinforced concrete frame-shear wall structure driven by random seismic excitations, are presented to verify the efficacy of the proposed method for seismic reliability evaluation of complex nonlinear structures.

Nonlinear random seismic response analysis of the double-trough aqueduct based on fiber beam element model

As an important lifeline project, large reinforced concrete aqueduct structures sometimes pass through areas with high seismic intensity. Therefore, the aqueduct structure is susceptible to earthquake damage or destruction during the water conveyance process, resulting in interruption of water conveyance and major safety accidents. In fact, because concrete is a multiphase composite material, it has obvious nonlinear and random characteristics. At the same time, seismic excitation is also naturally random due to differences in frequency spectrum and duration. Based on this, this paper uses the concrete elastoplastic random damage constitutive relationship and the random seismic excitation model to carry out the random nonlinear seismic response analysis of the double-trough aqueduct structure. The thin-walled characteristics of the girder section of the aqueduct structure is significantly different from that of the general bridge structure, and there is a certain error in the simulation of the seismic response of the aqueduct with traditional beam elements. Therefore, this paper combines the refined fiber beam element model, compiles the TCL language program suitable for the OpenSEES open analysis platform, and establishes the refined fiber beam finite element model of the aqueduct structure based on the random damage constitutive relationship of the concrete. The study of the response law and failure mechanism of aqueduct structures considering the coupling of concrete nonlinearity and seismic excitation randomness provides an important theoretical basis for the seismic optimization design of large-scale aqueduct structures.

Stochastic optimization of uncertain viscous dampers for energy-dissipation structures under random seismic excitations

Energy-dissipation devices have been widely used for seismic mitigation of civil structures. Stochastic optimization of energy-dissipation devices has emerged as an appealing means to achieve optimal seismic performance of structures in uncertain environment. This paper proposes an effective optimization framework for nonlinear viscous dampers of large-scale structures in consideration of both random seismic excitations and uncertain damper parameters. A dimension-reduced explicit time-domain method (ETDM) is employed for nonlinear time-history analysis of seismic responses and response sensitivities with respect to the nominal parameters of uncertain viscous dampers. To obtain the statistical moments of critical responses and the corresponding moment sensitivities, the high-efficient ETDM is then used in conjunction with the Monte-Carlo simulation (MCS) with sufficient samples of seismic excitation and damper parameters. The stochastic response and sensitivity results are further utilized for stochastic optimization of the nominal values of damper parameters with the method of moving asymptotes (MMA). The present optimization framework represents a hybrid approach combining the existing ETDM, MCS and MMA. A large-scale suspension bridge installed with nonlinear viscous dampers with uncertain parameters is analyzed to demonstrate the feasibility of the proposed optimization framework, and the influence of the uncertainties of damper parameters on stochastic optimization is also investigated.

Stochastic response control of particle dampers under random seismic excitation

In this paper, stochastic response control of particle damper system that is subjected to random seismic excitation is studied and the corresponding damping mechanism is further discussed. Based on the principle of multi-particle damper equivalent to a single particle damper, the nonlinear particle damper is equivalent to a linear system by the equivalent linearization method, and the mathematical expression of stochastic response of the particle damper system is obtained. The non-stationary response and stationary response of the particle damper system are subsequently compared, and the parametric study is conducted based on the stationary response of the particle damper system. It is shown that for a given particle damper system under random seismic excitation, there is an optimal gap clearance to minimize the structural response and this is the key parameter; the mass ratio is closely related to the gap clearance and in practice, the appropriate mass ratio should be properly selected; particle damper can also suppress the vibration response of the primary structure well over a wide frequency range, showing its strong robustness. Certain design suggestions are herein proposed. Finally, a numerical analysis and an experimental study are carried out to verify the viability and reliability of the stochastic vibration analysis of the particle damper system.

Nonlinear random seismic analysis of 3D high-speed railway track-bridge system based on OpenSEES

A new nonlinear track-bridge random model was established based on OpenSEES, of which the random seismic responses is systematically studied by using probability density evolution method (PDEM). First, a three-dimensional detail nonlinear random dynamic model of the track-bridge coupled system in high-speed railway is established considering the earthquake as the random excitation. The dynamic model is composed with the rail, CRTS II slab ballastless track, the simple supported bridges, bearing, pier and the pile foundation, from which the random dynamic equation of the random model is formulated. In order to evaluate the seismic performance of track structures from a random perspective, the random seismic responses of high-speed railway bridge under random seismic excitations are investigated and analyzed by using the PDEM. Eventually, the Newmark β integration method and the double edge difference method of TVD format are adopted to obtain the random responses involving the probability functions, which can be translated to get the mean value and the standard deviation of responses. Thus, the abundant probability information of seismic responses of the high-speed railway bridge under random seismic excitations can be obtained. The PDF and CDF of the sliding layer are obtained; thus, the failure probability and reliability of different damage grades of sliding layer are obtained. Discussions and significant conclusions on the random dynamic responses are presented.

Topology optimisation of truss structures under non-stationary random seismic excitations with displacement and stress constraints

This paper studies topology optimisation problems of truss structures under non-stationary random seismic excitations considering displacement and stress constraints. The optimisation model of truss structures is formulated by taking volume minimisation with constraints on variances of displacements and stresses. The explicit time domain method (ETDM) is applied to analyse the stochastic responses of the structure and the sensitivities with respect to the design variables. Based on the sensitivity analysis, the nodal positions and the cross-sectional areas of the bar elements of the truss structures are optimised simultaneously by using the globally convergent method of moving asymptotes (GCMMA). Meanwhile, a scheme is proposed to delete zero bars and redundant nodes during the optimisation process. Finally, several topology optimisation examples of 2-D and 3-D truss structures illustrate the accuracy and computational efficiency of the proposed method.

Topology optimisation of truss structures under non-stationary random seismic excitations with displacement and stress constraints

Topology optimisation of truss structures under non-stationary random seismic excitations with displacement and stress constraints

Vulnerability assessment of structures with stochastic properties subjected to random seismic excitation

The present work is concerned with assessing the vulnerability of seismically excited structures using non-deterministic analysis concepts, in order to take uncertainties into account. In this respect, uncertainties in both structural properties and earthquake loads are considered. Hence, the variation characteristics of uncertain material parameters along the length of frame members are modelled using Gaussian stochastic fields. Moreover, non-Gaussian probabilistic earthquake loading is assumed, which is described with the use of random variables based on data obtained from natural ground motion records. This modelling of uncertain-ties using random variables and fields is implemented in the framework of the direct Monte Carlo simulation method, in order to calculate structural response statistics for multi-storey frames with stochastic properties subjected to random seismic excitation.

Genetic algorithm-based integrated optimization of active control systems for civil structures subjected to random seismic excitations

An efficient genetic algorithm-based approach is developed to solve the integrated optimization problem for active control systems of civil structures under random seismic excitations. Not only the number and location of actuators but also the control algorithm can be optimized simultaneously by a novel genetic algorithm while the randomness of seismic excitations is taken into account. In view of the randomness of earthquake actions, optimal control criteria should be established in a probabilistic sense. Considering the trade-off between control effectiveness and energy consumption, two sets of probabilistic criteria for stochastic optimal control of structures are therefore developed, on the basis of peak and root-mean-square values of objective quantities. In the proposed genetic algorithm, an effective selection policy, an improved binary single-point crossover and a new single-locus or two-locus mutation are adopted. Finally, the effectiveness, efficiency and stability of the proposed optimization methodology are verified by two numerical examples.