Derivation of response spectrum compatible non-stationary stochastic processes relying on Monte Carlo-based peak factor estimation

In this paper a novel non-iterative approach is proposed to address the problem of deriving non-stationary stochastic processes which are compatible in the mean sense with a given (target) response (uniform hazard) spectrum (UHS) as commonly desired in the aseismic structural design regulated by contemporary codes of practice. This is accomplished by solving a standard over-determined minimization problem in conjunction with appropriate median peak factors. These factors are determined by a plethora of reported new Monte Carlo studies which on their own possess considerable stochastic dynamics merit. In the proposed approach, generation and treatment of samples of the processes individually on a deterministic basis is not required as is the case with the various approaches found in the literature addressing the herein considered task. The applicability and usefulness of the approach is demonstrated by furnishing extensive numerical data associated with the elastic design UHS of the current European (EC8) and the Chinese (GB 50011) aseismic code provisions. Purposely, simple and thus attractive from a practical viewpoint, uniformly modulated processes assuming either the Kanai-Tajimi (KT) or the Clough-Penzien (C-P) spectral form are employed. The Monte Carlo studies yield damping and duration dependent median peak factor spectra, given in a polynomial form, associated with the first passage problem for UHS compatible K-T and C-P uniformly modulated stochastic processes. Hopefully, the herein derived stochastic processes and median peak factor spectra can be used to facilitate the aseismic design of structures regulated by contemporary code provisions in a Monte Carlo simulation based or stochastic dynamics-based context of analysis

Optimum design of the tuned mass-damper-inerter for serviceability limit state performance in wind-excited tall buildings

Optimally designed tuned mass-damper-inerters (TMDIs) are considered to meet code-prescribed serviceability criteria in typical wind-excited tall buildings subject to vortex shedding effects in a performance-based design context. The TMDI, couples the classical tuned-mass-damper (TMD) with an inerter, a two-terminal device resisting the relative acceleration of its terminals, achieving mass-amplification and higher-modes-damping effects compared to the TMD. A benchmark 74-storey building is considered, where TMDI is added to the structural system assuming ideal linear inerter behavior. The wind action is defined through a non-diagonal power spectral density matrix supporting computationally efficient frequency domain structural analyses. The TMDI is optimally designed for stiffness, damping, and inerter constant parameters via a standard numerical optimization search, for a range of pre-specified attached TMDI mass values. It is shown that the TMDI achieves more lightweight construction in the design of new code-compliant tall buildings against wind

Assessment of sub-Nyquist deterministic and random data sampling techniques for operational modal analysis

This paper assesses numerically the potential of two different spectral estimation approaches supporting non-uniform in time data sampling at sub-Nyquist average rates (i.e., below the Nyquist frequency) to reduce data transmission payloads in wireless sensor networks (WSNs) for operational modal analysis (OMA) of civil engineering structures. This consideration relaxes transmission bandwidth constraints in WSNs and prolongs sensor battery life since wireless transmission is the most energy-hungry on-sensor operation. Both the approaches assume acquisition of sub-Nyquist structural response acceleration measurements and transmission to a base station without on-sensor processing. The response acceleration power spectral density matrix is estimated directly from the sub-Nyquist measurements and structural mode shapes are extracted using the frequency domain decomposition algorithm. The first approach relies on the compressive sensing (CS) theory to treat sub-Nyquist randomly sampled data assuming that the acceleration signals are sparse/compressible in the frequency domain (i.e., have a small number of Fourier coefficients with significant magnitude). The second approach is based on a power spectrum blind sampling (PSBS) technique considering periodic deterministic sub-Nyquist “multi-coset” sampling and treating the acceleration signals as wide-sense stationary stochastic processes without posing any sparsity conditions. The modal assurance criterion (MAC) is adopted to quantify the quality of mode shapes derived by the two approaches at different sub-Nyquist compression rates (CRs) using computer-generated signals of different sparsity and field-recorded stationary data pertaining to an overpass in Zurich, Switzerland. It is shown that for a given CR, the performance of the CS-based approach is detrimentally affected by signal sparsity, while the PSBS-based approach achieves MAC>0.96 independently of signal sparsity for CRs as low as 11% the Nyquist rate. It is concluded that the PSBS-based approach reduces effectively data transmission requirements in WSNs for OMA, without being limited by signal sparsity and without requiring a priori assumptions or knowledge of signal sparsity

Optimal design of a novel tuned mass-damper-inerter (TMDI) passive vibration control configuration for stochastically support-excited structural systems

This paper proposes a novel passive vibration control configuration, namely the tuned mass-damper-inerter (TMDI), introduced as a generalization of the classical tuned mass-damper (TMD), to suppress the oscillatory motion of stochastically support excited mechanical cascaded (chain-like) systems. The TMDI takes advantage of the "mass amplification effect" of the inerter, a two-terminal flywheel device developing resisting forces proportional to the relative acceleration of its terminals, to achieve enhanced performance compared to the classical TMD. Specifically, it is analytically shown that optimally designed TMDI outperforms the classical TMD in minimizing the displacement variance of undamped single-degree-of-freedom (SDOF) white-noise excited primary structures. For this particular case, optimal TMDI parameters are derived in closed-form as functions of the TMD mass and the inerter constant. Furthermore, pertinent numerical data are furnished, derived by means of a numerical optimization procedure, for a 3-DOF classically damped primary structure base excited by stationary colored noise, which exemplify the effectiveness of the TMDI over the classical TMD to suppress the fundamental mode of vibration for MDOF structures. It is concluded that the incorporation of the inerter in the proposed TMDI configuration can either replace part of the TMD vibrating mass to achieve lightweight passive vibration control solutions, or improve the performance of the classical TMD for a given TMD mass

Effective linear damping and stiffness coefficients of nonlinear systems for design spectrum based analysis

A stochastic approach for obtaining reliable estimates of the peak response of nonlinear systems to excitations specified via a design seismic spectrum is proposed. This is achieved in an efficient manner without resorting to numerical integration of the governing nonlinear equations of motion. First, a numerical scheme is utilized to derive a power spectrum which is compatible in a stochastic sense with a given design spectrum. This power spectrum is then treated as the excitation spectrum to determine effective damping and stiffness coefficients corresponding to an equivalent linear system (ELS) via a statistical linearization scheme. Further, the obtained coefficients are used in conjunction with the (linear) design spectrum to estimate the peak response of the original nonlinear systems. The cases of systems with piecewise linear stiffness nonlinearity, along with bilinear hysteretic systems are considered. The seismic severity is specified by the elastic design spectrum prescribed by the European aseismic code provisions (EC8). Monte Carlo simulations pertaining to an ensemble of nonstationary EC8 design spectrum compatible accelerograms are conducted to confirm that the average peak response of the nonlinear systems compare reasonably well with that of the ELS, within the known level of accuracy furnished by the statistical linearization method. In this manner, the proposed approach yields ELS which can replace the original nonlinear systems in carrying out computationally efficient analyses in the initial stages of the aseismic design of structures under severe seismic excitations specified in terms of a design spectrum

A novel stochastic linearization framework for seismic demand estimation of hysteretic MDOF systems subject to linear response spectra

This paper proposes a novel computationally economical stochastic dynamics framework to estimate the peak inelastic response of yielding structures modelled as nonlinear multi degreeof-freedom (DOF) systems subject to a given linear response spectrum defined for different damping ratios. This is accomplished without undertaking nonlinear response history analyses (RHA) or, to this effect, constructing an ensemble of spectrally matched seismic accelerograms. The proposed approach relies on statistical linearization and enforces pertinent statistical conditions to decompose the inelastic d-DOF system into d linear single DOF oscillators with effective linear properties (ELPs): natural frequency and damping ratio. Each such oscillator is subject to a different stationary random process compatible with the excitation response spectrum with damping ratio equal to the oscillator effective critical damping ratio. This equality is achieved through a small number of iterations to a pre-specified tolerance, while peak inelastic response estimates for all DOFs of interest are obtained by utilization of the excitation response spectrum in conjunction with the ELPs. The applicability of the proposed framework is numerically illustrated using a 3-storey Bouc-Wen hysteretic frame structure exposed to the Eurocode 8 elastic response spectrum. Nonlinear RHA involving a large ensemble of non-stationary Eurocode 8 spectrum compatible accelerograms is conducted to assess the accuracy of the proposed approach in a Monte Carlo-based context. It is found that the novel feature of iterative matching between the excitation response spectrum damping ratio and the ELP damping ratio reduces drastically the error of the estimates (i.e., by an order of magnitude) obtained by non-iterative application of the framework

Optimal tuned mass-damper-inerter (TMDI) design in wind-excited tall buildings for occupants’ comfort serviceability performance and energy harvesting

The tuned mass-damper-inerter (TMDI) couples the classical tuned mass-damper (TMD), with an inerter device developing a resisting force proportional to the relative acceleration of its ends by the “inertance” constant. Previous works demonstrated that the inclusion of the TMDI leads to more efficient broadband vibration control for a range of different structures under different actions. This paper proposes a novel optimal TMDI design formulation to address occupants’ comfort in wind-excited slender tall buildings susceptible to vortex shedding (VS) effects and to explore optimal TMDI’s potential for transforming part of the windinduced kinetic energy to usable electricity in tall buildings. Attention is focused on investigating benefits of TMDIs with different inertial properties (i.e., secondary mass/weight and inertance) configured in different topologies defined by the number of floors spanned by the inerter device to connect the secondary mass to the building structure. Optimally designed TMDIs for a wide range of inertial properties and three different topologies are obtained through numerical solution of the underlying optimization problem for a benchmark 305.9m tall building with more than 6 height-to-width ratio subjected to experimentally calibrated spatiallycorrelated across-wind force field accounting for VS effects. Performance-based design (PBD) graphs on the TMDI inertial (mass-inertance) plane are furnished demonstrating that any fixed structural performance level in terms of occupants’ comfort (i.e., peak top floor acceleration) can be achieved through lightweight TMDIs if compared with classical TMDs as long as sufficient inertance is provided. Further, TMDI robustness to host structure properties and to reference wind velocity is shown to increase by increasing inertance or by spanning more floors in connecting the secondary mass with the host structure by the inerter. Lastly, it is found that increased available energy for harvesting in wind excited tall buildings is achieved by incorporating electromagnetic motors in TMDIs with varying damping property, while concurrent reduced floor acceleration and increased available energy for harvesting is accomplished by TMDI topologies with inerters spanning more floors

Wavelet based response spectrum compatible synthesis of accelerograms and statistical linearization based analysis of the peak response of inelastic systems

A novel method for producing seismic accelerograms whose response spectra comply with the pertinent seismic code criteria has been proposed. It encompasses a stochastic dynamics formulation for defining an evolutionary power spectrum that is related to a given design (target) spectrum in a statistical sense, and a deterministic harmonic wavelet-based procedure to iteratively modify seismic accelerograms on an individual basis. The incorporation of the stochastic dynamics formulation allows for generating ensembles of artificial design spectrum compatible accelerograms, without the need to consider any recorded strong ground motion. Several such ensembles pertaining to the design spectrum prescribed by the European aseismic code provisions (EC8) are provided. Moreover, in the developed wavelet-based procedure the unique attributes of harmonic wavelets are exploited to "surgically" modify the frequency content of seismic accelerograms to meet the commonly prescribed compatibility criteria. An example involving the modification of a suite of real recorded accelerograms to be used for the design of base-isolated buildings according to the EC8 code provisions is included. Appropriate wavelet-based joint time-frequency analysis of the original and of the modified signals have been provided suggesting that the modified signals maintain the main patterns of the evolutionary frequency content of the original accelerograms. Appended to the above a computationally efficient methodology is suggested for estimating the maximum seismic response of nonlinear systems exposed to excitations specified by a given design spectrum. Specifically, stationary design spectrum compatible power spectra are considered in conjunction with the method of statistical linearization to derive effective linear stiffness and damping properties associated with certain nonlinear oscillators. The cases of Duffing bilinear hysteretic, and smooth hysteretic systems described by the Bouc-Wen differential model are considered. It is found via pertinent Monte Carlo analyses that the peak response of the nonlinear and of the derived equivalent linear systems compare reasonably well. Furthermore, it is shown through appropriate numerical examples that the latter methodology is capable of deriving inelastic response spectra from elastic design spectra without the need to integrate numerically the underlying nonlinear equations of motion