White Noise Base Excitation Research Articles

On the selection of user-defined parameters in data-driven stochastic subspace identification

Abstract The paper focuses on the time domain output-only technique called Data-Driven Stochastic Subspace Identification (DD-SSI); in order to identify modal models (frequencies, damping ratios and mode shapes), the role of its user-defined parameters is studied, and rules to determine their minimum values are proposed. Such investigation is carried out using, first, the time histories of structural responses to stationary excitations, with a large number of samples, satisfying the hypothesis on the input imposed by DD-SSI. Then, the case of non-stationary seismic excitations with a reduced number of samples is considered. In this paper, partitions of the data matrix different from the one proposed in the SSI literature are investigated, together with the influence of different choices of the weighting matrices. The study is carried out considering two different applications: (1) data obtained from vibration tests on a scaled structure and (2) in-situ tests on a reinforced concrete building. Referring to the former, the identification of a steel frame structure tested on a shaking table is performed using its responses in terms of absolute accelerations to a stationary (white noise) base excitation and to non-stationary seismic excitations of low intensity. Black-box and modal models are identified in both cases and the results are compared with those from an input-output subspace technique. With regards to the latter, the identification of a complex hospital building is conducted using data obtained from ambient vibration tests.

Optimal design of Nonlinear Energy Sinks for SDOF structures subjected to white noise base excitations

Abstract Nonlinear Energy Sinks (NESs) have recently received increasing attention from researchers because of their capability to passively absorb a significant amount of energy over a wide range of frequencies. In most studies, the dynamic response of the main structure coupled with one or more NESs is analysed for impulsive loading. In this paper, the performance of the NES attached to a Single Degree of Freedom (SDOF) system, under random Gaussian white noise base excitations, is investigated through several numerical simulations. In order to determine the optimal configuration for the device, four different objective functions are considered. Sensitivity analyses with respect to the intensity of the random loads, the mass ratio and the main parameters of the primary structure are presented. The authors propose an approximate design approach based on the use of the Statistical Linearization Technique, and an accurate empirical formulation linking the NES optimal parameters to the characteristic of the main structure and the random excitation. Numerical results are validated by Monte Carlo simulations. Finally, a numerical application for a 2-DOFs system equipped with a NES has been presented in order to investigate the applicability of the proposed empirical approach for Multi Degrees of Freedom structures.

Limits on the power available to harvest from broadband random excitation

With the large diversity in energy harvesters aiming to extract maximum power from broadband excitations, it is important to know what the maximum power achievable is. This paper derives new upper bounds on the available power for a harvester with general nonlinear stiffness coupled to a nonlinear electrical circuit. White noise base excitations are known to input power proportional to the total oscillating mass of the system and the magnitude of the spectral density of the noise regardless of the details of the oscillating system. This power is split between undesirable mechanical damping and useful electrical dissipation with the form of the stiffness profile and device parameters determining the relative proportions in each dissipation mechanism. An upper bound on electrical power is sought and, provided certain conditions are met, shown to be a simple function of relatively few system parameters and, importantly, independent of the stiffness profile or electrical nonlinearity.The benefits of knowing the upper limits on power are threefold: to guide optimal harvester design, to assess how close to optimal current devices are and to provide a preliminary estimation of the harvester mass necessary in a given operating environment for a given power requirement.

Earthquake Excited Base-Isolated Structures Protected by Tuned Liquid Column Dampers: Design Approach and Experimental Verification

In this contribution a direct approach for optimal design of a Tuned Liquid Column Damper (TLCD) device attached to the base slab of a base-isolated structure is presented, aiming at reducing the seismic displacement demand of the base-isolation subsystem. Assuming white noise base excitation, for a wide parameter range a direct optimization procedure yields design charts for optimal TLCD quantities. The performance of the base-isolated structure equipped with optimally tuned TLCD device in comparison to the simple base-isolated one is evaluated both numerically and experimentally. In a numerical study the system is subjected to the 44 records of the FEMA P-695 far-field ground motion set. The experimental studies are conducted on a three-story small-scale base-isolated shear frame model. From the results it can be concluded that a TLCD effectively controls the seismic response of earthquake excited low-damped base-isolated structures.

Shake table testing of an elevator system in a full‐scale five‐story building

This paper investigates the seismic performance of a functional traction elevator as part of a full-scale five-story building shake table test program. The test building was subjected to a suite of earthquake input motions of increasing intensity, first while the building was isolated at its base, and subsequently while it was fixed to the shake table platen. In addition, low-amplitude white noise base excitation tests were conducted while the elevator system was placed in three different configurations, namely, by varying the vertical location of its cabin and counterweight, to study the acceleration amplifications of the elevator components due to dynamic excitations. During the earthquake tests, detailed observation of the physical damage and operability of the elevator as well as its measured response are reported. Although the cabin and counterweight sustained large accelerations due to impact during these tests, the use of well-restrained guide shoes demonstrated its effectiveness in preventing the cabin and counterweight from derailment during high-intensity earthquake shaking. However, differential displacements induced by the building imposed undesirable distortion of the elevator components and their surrounding support structure, which caused damage and inoperability of the elevator doors. It is recommended that these aspects be explicitly considered in elevator seismic design.

Influence of the construction process and nonstructural components on the modal properties of a five‐story building

SummaryA full‐scale five‐story reinforced concrete building was built and tested on the NEES‐UCSD shake table during the period from May 2011 to May 2012. The purpose of this test program was to study the response of the structure and nonstructural components and systems (NCSs) and their dynamic interaction during seismic base excitation of different intensities. The building specimen was tested first under a base‐isolated condition and then under a fixed‐based condition. As the building was being erected, an accelerometer array was deployed on the specimen to study the evolution of its modal parameters during the construction process and placement of major NCSs. A sequence of dynamic tests, including daily ambient vibration, shock (free vibration) and forced vibration tests (low‐amplitude white noise and seismic base excitations), were performed on the building at different stages of construction. Different state‐of‐the‐art system identification methods, including three output‐only and two input‐output methods, were used to estimate the modal properties of the building. The obtained results allow to investigate in detail the effects of the construction process and NCSs on the dynamic parameters of this building system and to compare the modal properties obtained from different methods, as well as the performance of these methods. Copyright © 2015 John Wiley & Sons, Ltd.

Localized Discrete Modelling of Contact Interfaces to Predict the Dynamic Behaviour of Assembled Structures under Random Excitation

Joints used to fasten different parts are the source of local non-linearity with predominance of contact damping in comparison to inherent material damping. The conventional numerical models can predict the dynamic behaviour to a good accuracy, but their implementation for the large system under real time dynamic excitations - like random vibration are encountered with problems of numerical convergence and high computational cost. This paper proposes an approach to model the contact interfaces using discrete elements, with a non-homogeneous definition for the equivalent contact stiffness and damping over the contact interface. The non-homogeneous definition captures the non-linear effects and the local linearisation provides the capability to perform the frequency domain analysis for non-deterministic excitations. The proposed model is validated with experimental results for a test structure excited with random white noise base excitation.

System identification of a full‐scale five‐story reinforced concrete building tested on the NEES‐UCSD shake table

This paper presents the identification of modal properties of a full-scale five-story reinforced concrete building fully outfitted with nonstructural components and systems (NCSs) tested on the NEES-UCSD shake table. The fixed base building is subjected to a sequence of earthquake motions selected to progressively damage the structure and NCSs. Between seismic tests, ambient vibration response is recorded. Additionally, low-amplitude white noise (WN) base excitation tests are conducted during the test protocol. Using the vibration data recorded, five state-of-the-art system identification (SID) methods are employed, including three output-only and two input-output. These methods are used to estimate the modal properties of an equivalent viscously-damped linear elastic time-invariant model of the building at different levels of damage and their results compared. The results show that modal properties identified from different methods are in good agreement and that the estimated modal parameters are affected by the amplitude of excitation and structural/nonstructural damage. Detailed visual inspections of damage performed between the seismic tests permit correlation of the identified modal parameters with the actual damage. The identified natural frequencies are used to determine the progressive loss of apparent global stiffness of the building, and the state-space models identified using WN test data are employed to investigate the relative modal contributions to the measured building response at different damage states. This research provides a unique opportunity to investigate the performance of different SID methods when applied to vibration data recorded in a real building subjected to progressive damage induced by a realistic source of dynamic excitation. Copyright © 2015 John Wiley & Sons, Ltd.

Dynamic characteristics and seismic behavior of prefabricated steel stairs in a full‐scale five‐story building shake table test program

SummaryThis paper investigates the dynamic characteristics and seismic behavior of prefabricated steel stairs in a full‐scale five‐story building shake table test program. The test building was subjected to a suite of earthquake input motions and low‐amplitude white noise base excitations first, while the building was isolated at its base, and subsequently while it was fixed to the shake table platen. This paper presents the modal characteristics of the stairs identified using the data recorded from white noise base excitation tests as well as the physical and measured responses of the stairs from the earthquake tests. The observed damage to the stairs is categorized into three distinct damage states and is correlated with the interstory drift demands of the building. These shake table tests highlight the seismic vulnerability of modern designed stair systems and in particular identifies as a key research need the importance of improving the deformability of flight‐to‐building connections. Copyright © 2015 John Wiley & Sons, Ltd.

Finite-Element Model Updating for Assessment of Progressive Damage in a 3-Story Infilled RC Frame

AbstractThis paper presents a study on the identification of progressive damage, using an equivalent linear finite-element model updating strategy, in a masonry infilled RC frame that was tested on a shake table. A two-thirds-scale, 3-story, 2-bay, infilled RC frame was tested on the UCSD–NEES shake table to investigate the seismic performance of this type of construction. The shake table tests induced damage in the structure progressively through scaled historical earthquake records of increasing intensity. Between the earthquake tests and at various levels of damage, low-amplitude white-noise base excitations were applied to the infilled RC frame. In this study, the effective modal parameters of the damaged structure have been identified from the white-noise test data with the assumption that it responded in a quasi-linear manner. Modal identification has been performed using a deterministic-stochastic subspace identification method based on the measured input–output data. A sensitivity-based finite-ele...

System Identification Study of a 7-Story Full-Scale Building Slice Tested on the UCSD-NEES Shake Table

A full-scale 7-story reinforced concrete building slice was tested on the unidirectional University of California–San Diego Network for Earthquake Engineering Simulation (UCSD-NEES) shake table during the period from October 2005 to January 2006. A rectangular wall acted as the main lateral force resisting system of the building slice. The shake table tests were designed to damage the building progressively through four historical earthquake records. The objective of the seismic tests was to validate a new displacement-based design methodology for reinforced concrete shear wall building structures. At several levels of damage, ambient vibration tests and low-amplitude white noise base excitation tests were applied to the building, which responded as a quasi-linear system with dynamic parameters evolving as a function of structural damage. Six different state-of-the-art system identification algorithms, including three output-only and three input-output methods were used to estimate the modal parameters (natural frequencies, damping ratios, and mode shapes) at different damage levels based on the response of the building to ambient as well as white noise base excitations, measured using DC-coupled accelerometers. The modal parameters estimated at various damage levels using different system identification methods are compared to (1) validate/cross-check the modal identification results and study the performance of each of these system identification methods, and to (2) investigate the sensitivity of the identified modal parameters to actual structural damage. For a given damage level, the modal parameters identified using different methods are found to be in good agreement, indicating that these estimated modal parameters are likely to be close to the actual modal parameters of the building specimen.

Damage identification study of a seven-story full-scale building slice tested on the UCSD-NEES shake table

A full-scale seven-story reinforced concrete building section was tested on the UCSD-NEES shake table during the period October 2005–January 2006. The shake table tests were designed to damage the building progressively through four historical earthquake records. At various levels of damage, ambient vibration tests and low-amplitude white noise base excitations with root-mean-square accelerations of 0.03 g and 0.05 g were applied to the building, which responded as a quasi-linear system with parameters evolving as a function of structural damage. Modal parameters (natural frequencies, damping ratios and mode shapes) of the building were identified at different damage levels based on the response of the building to ambient as well as low-amplitude white noise base excitations, measured using DC coupled accelerometers. This paper focuses on damage identification of this building based on changes in identified modal parameters. A sensitivity-based finite element model updating strategy is used to detect, localize and quantify damage at each damage state considered. Three sets of damage identification results are obtained using modal parameters identified based on ambient, 0.03 g, and 0.05 g RMS white noise test data, respectively. The damage identification results obtained in all three cases do not exactly coincide, but they are consistent with the concentration of structural damage observed at the bottom two stories of the building. The difference in the identified damage results is mainly due to the significant difference in the identified modal parameters used in the three cases. The assumption of a quasi-linear dynamic system is progressively violated with increasing level of excitation. Therefore, application of nonlinear FE model updating strategies is recommended in future studies to resolve the errors caused by structural response nonlinearity.

Passive Vibration Control: A Probabilistic Approach

This paper is concerned with the behavior of vibration absorbers attached to systems with uncertain properties. The uncertainties of the main system properties are modeled in a probabilistic sense by means of a Bayesian probabilistic interpretation. The structural systems considered in this study are simple systems modeled as one-degree-of-freedom oscillators subjected to a white noise base excitation. Due to the uncertainty of the main system properties, the classical deterministic minimization problem becomes a stochastic optimization problem. An optimization technique is implemented to solve this non-classical problem, and the absorber parameters as well as the optimum response of the system are obtained. These results are then used to assess the performance of the vibration absorber. It is found that parameter uncertainties may have a significant effect on its effectiveness. Finally, an alternative approach that improves the absorber efficiency, when uncertainties in the main system properties are considered, is presented in this paper.

Stability of frames subjected to a white noise base excitation

Dynamic stability of elastic frames subjected to an earthquake Gaussian white noise base excitation is considered. Different necessary and sufficient conditions for the mean-square stability of the equilibrium state are developed. Several examples concerning the stability of the equilibrium state of single and multi-degree-of-freedom structures are studied. The results are compared with those obtained by a digital simulation technique and the existing almost-sure stability criteria. The simulation results suggest that the mean-square stability is more reliable when compared with the almost-sure one.

Response of Two-Degree-of-Freedom Systems to White Noise Base Excitation

The response of a coupled two-degree-of-freedom system to white noise excitation is obtained analytically for a wide variation of the dimensionless parameters of the system. The interrelations of these parameters on the response are illustrated and shown to be very significant when the uncoupled natural frequencies of the system are of the same order. The limitations of approximation methods based on single-degree-of-freedom system or uncoupled two-degree-of-freedom system models are indicated. The applicability of the study to dynamic vibration absorber principles is evident. The responses are compared to previously published results.

Response of Two Degree-of-Freedom Systems to White Noise Base Excitation

The response of a two degree-of-freedom system, consisting of a spring-mass-dashpot mounted on another spring-mass-dashpot, due to white noise motion of the base, is examined over the following ranges of system parameters: mass ratio, 0.01 ⩽ M ⩽ 1.0; damping factors, 0.01 ⩽ S1 ⩽ 0.10, 0.01 ⩽ S2 ⩽ 0.05; frequency ratio between uncoupled natural frequencies of each spring-mass-dashpot, 0.20 ⩽ W ⩽ 10.0. The response of many practical systems may be analyzed in terms of such systems. The lower mass may be visualized as a basic structure supporting equipment represented by the upper mass. Alternatively, the lower mass may be equipment, excited by the basic structure, with the upper mass representing chassis or components within. Analyses of such systems are often made on the assumption that the lower mass response is unaffected by the upper mass response, i.e., small mass ratio. The results presented explore the ranges of W and M over which such an approximation yields satisfactory results and indicate the magnitude of the errors in other ranges, particularly in the vicinity of W = 1.0, to which it may lead. The effectiveness of the upper mass as a “dynamic vibration absorber” for random excitation of the lower mass is demonstrated. The results for W = 1.0 are compared to previously published experimental results.