scholarly journals Model-Free Identification of Nonlinear Restoring Force with Modified Observation Equation

2019 ◽  
Vol 9 (2) ◽  
pp. 306 ◽  
Author(s):  
Jia He ◽  
Xiaoxiong Zhang ◽  
Mengchen Qi ◽  
Bin Xu
Keyword(s):  
Nonlinear Process ◽  
Observation Equation ◽  
Building Structures ◽  
Time Step ◽  
Engineering Structures ◽  
Restoring Force ◽  
Nonparametric Models ◽  
Nonlinear Restoring Force ◽  
Model Free ◽  
Nonparametric Techniques

Nonlinearity exists widely in civil engineering structures; for example, the initiation and growth of damage under dynamic loadings is a typical nonlinear process. To date, for the purpose of structural evaluation and a better understanding nonlinear characteristics of complicated structures, a number of parametric and nonparametric methods have been developed for the identification of nonlinear restoring force (NRF). However, due to the highly individualistic nature of nonlinear systems, it would be inefficient to attempt to express the structural NRF in a general parametric form. For many nonparametric techniques, their nonparametric models or approximations may result in undesirable results or oscillations around unsmooth points. In this paper, on the basis of extended Kalman filter (EKF), a model-free NRF identification approach is proposed to circumvent the limitations mentioned above. The NRF to be identified was treated as ‘unknown fictitious input’, and thus, no prior assumptions or approximations for the NRF model were required. With the aid of a projection matrix, a modified version of observation equation was obtained. Based on the principle of EKF, the recursive solution of the proposed approach was analytically derived. The NRFs provided by the nonlinear components were identified by means of least squares estimation (LSE) at each time step. Numerical examples, including building structures equipped with magnetorheological (MR) damper and shape memory alloy (SMA) damper, demonstrated that the proposed approach is capable of satisfactorily identifying NRF without knowledge or intuitive assumptions of any nonlinear model class in advance.

Structural nonlinearity and mass identification with a nonparametric model using limited acceleration measurements

2018 ◽  
Vol 22 (4) ◽  
pp. 1018-1031 ◽  
Author(s):  
Bin Xu ◽  
Bai-Chuan Deng ◽  
Jing Li ◽  
Jia He
Keyword(s):  
Structural Damage ◽  
Nonparametric Model ◽  
Nonlinear Behaviour ◽  
Engineering Structures ◽  
Restoring Force ◽  
Damage Initiation ◽  
Nonlinear Restoring Force ◽  
Structural Nonlinearity ◽  
Identification Approach ◽  
Mass Identification

Structural nonlinearity identification is critical for post-event damage detection or condition evaluation of engineering structures after strong dynamic excitation such as earthquake where structural nonlinear behaviour should be considered. Structural nonlinear restoring force provides direct indicator describing structural damage initiation and development procedure. Considering the availability of structural dynamic response measurement and the difficulty in defining a parametric model for structural nonlinearity and in estimating structure mass accurately in practice, in this article, a time-domain structural nonlinear restoring force and mass identification approach for multi-degree-of-freedom structures under incomplete excitation using limited acceleration measurements but without using any parametric models of structural nonlinear restoring force is proposed. At first, a memory fading extended Kalman filter with a weighted globl iteration (MF-EKF-WGI) is used to identify the location of nonlinearities and then a Chebyshev polynomial nonparametric model is introduced to model the nonlinear restoring force. The unscented Kalman filter is used to identify the structural responses and the parameters of the Chebyshev polynomial to describe structural nonlinearity. Numerical and experimental studies with a four-storey frame model structure equipped with a magnetorheological damper, which is employed to mimic structural nonlinear behaviour, under impact excitations are carried out to validate the performance of the proposed approach using acceleration measurements at certain degrees of freedom. Numerical and experimental results show that the proposed approach is capable of identifying both structural nonlinear restoring force and mass with acceptable accuracy even with a very rough initial mass estimation. The proposed time-domain identification approach can be used to detect structural damage initiation and development process and to evaluate energy consumption quantitatively of engineering structures under dynamic loadings.

Nonparametric nonlinear restoring force and excitation identification with Legendre polynomial model and data fusion

2021 ◽  
pp. 147592172199474
Author(s):  
Bin Xu ◽  
Ye Zhao ◽  
Baichuan Deng ◽  
Yibang Du ◽  
Chen Wang ◽  
...  
Keyword(s):  
Data Fusion ◽  
Legendre Polynomial ◽  
Structural Parameters ◽  
Polynomial Model ◽  
Magnetorheological Damper ◽  
Dynamic Responses ◽  
Identification Accuracy ◽  
Restoring Force ◽  
Nonlinear Restoring Force ◽  
Dynamic Loadings

Identification of nonlinear restoring force and dynamic loadings provides critical information for post-event damage diagnosis of structures. Due to high complexity and individuality of structural nonlinearities, it is difficult to provide an exact parametric mathematical model in advance to describe the nonlinear behavior of a structural member or a substructure under strong dynamic loadings in practice. Moreover, external dynamic loading applied to an engineering structure is usually unknown and only acceleration responses at limited degrees of freedom of the structure are available for identification. In this study, a nonparametric nonlinear restoring force and excitation identification approach combining the Legendre polynomial model and extended Kalman filter with unknown input is proposed using limited acceleration measurements fused with limited displacement measurements. Then, the performance of the proposed approach is first illustrated via numerical simulation with multi-degree-of-freedom frame structures equipped with magnetorheological dampers mimicking nonlinearity under direct dynamic excitation or base excitation using noise-polluted measurements. Finally, a dynamic experimental study on a four-story steel frame model equipped with a magnetorheological damper is carried out and dynamic response measurement is employed to validate the effectiveness of the proposed method by comparing the identified dynamic responses, nonlinear restoring force, and excitation force with the test measurements. The convergence and the effect of initial estimation errors of structural parameters on the final identification results are investigated. The effect of data fusion on improving the identification accuracy is also investigated.

Soft X-ray emission from an anharmonic collisional nanoplasma by a laser–nanocluster interaction

2021 ◽  
Vol 87 (3) ◽  
Author(s):  
R. Nemati Siahmazgi ◽  
S. Jafari
Keyword(s):  
Electric Field ◽  
Laser Beam ◽  
Resonant Frequency ◽  
Restoring Force ◽  
Cluster Radius ◽  
X Ray ◽  
Nonlinear Restoring Force ◽  
Cluster Temperature ◽  
Argon Clusters ◽  
Helium Neon

The purpose of the present paper is to investigate the generation of soft X-ray emission from an anharmonic collisional nanoplasma by a laser–nanocluster interaction. The electric field of the laser beam interacts with the nanocluster and leads to ionization of the cluster atoms, which then produces a nanoplasma. Because of the nonlinear restoring force in an anharmonic nanoplasma, the fluctuations and heating rate of, as well as the power radiated by, the electrons in the nanocluster plasma will be notably different from those arising from a linear restoring force. By comparing the nonlinear restoring force state (which arises from an anharmonic cluster) with that of the linear restoring force (in harmonic clusters), the cluster temperature specifically changes at the resonant frequency relative to the linear restoring force, while the variation of the anharmonic cluster radius is almost identical to that of the harmonic cluster radius. In addition, it is revealed that a sharp peak of X-ray emission arises after some picoseconds in deuterium, helium, neon and argon clusters.

scholarly journals Pounding Effects on the Earthquake Response of Adjacent Reinforced Concrete Structures Strengthened by Cable Elements

2014 ◽  
Vol 44 (2) ◽  
pp. 41-56 ◽  
Author(s):  
Angelos Liolios ◽  
Asterios Liolios ◽  
George Hatzigeorgiou ◽  
Stefan Radev
Keyword(s):  
Reinforced Concrete ◽  
Numerical Approach ◽  
Earthquake Response ◽  
Existing Buildings ◽  
The Finite Element Method ◽  
Time Step ◽  
Engineering Structures ◽  
Rc Structures ◽  
Incremental Approach ◽  
Rc Frames

Abstract A numerical approach for estimating the effects of pounding (seismic interaction) on the response of adjacent Civil Engineering structures is presented. Emphasis is given to reinforced concrete (RC) frames of existing buildings which are seismically strengthened by cable-elements. A double discretization, in space by the Finite Element Method and in time by a direct incremental approach is used. The unilateral behaviours of both, the cable-elements and the interfaces contact-constraints, are taken strictly into account and result to inequality constitutive conditions. So, in each time-step, a non-convex linear complementarity problem is solved. It is found that pounding and cable strengthening have significant effects on the earthquake response and, hence, on the seismic upgrading of existing adjacent RC structures.

Bergsprungur og byggingar á höfuðborgarsvæðinu

2018 ◽  
Vol 24 ◽  
pp. 25-29
Author(s):  
Páll Einarsson ◽  
Haukur Jóhannesson ◽  
Ásta Rut Hjartardóttir
Keyword(s):  
Metropolitan Area ◽  
Urban Areas ◽  
Structural Damage ◽  
Seismic Waves ◽  
Relative Displacement ◽  
Building Structures ◽  
Engineering Structures ◽  
Volcanic System ◽  
Tectonic Plates ◽  
Building Practice

Straddling the boundary between two of the major tectonic plates on Earth, Iceland offers unique conditions for engineering structures that require special attention. Urban areas are rapidly expanding into areas where the bedrock is cut by numerous active fractures and faults. The fissure swarm of the Krísuvík volcanic system runs through the outskirts of Reykjavík and other towns of the metropolitan area. Activity of its fractures mostly occurs during magmatic events along the Reykjanes Peninsula oblique rift on a thousand years timescale. Hazard caused by the fractures is mostly twofold: Relative displacement of the walls of the fracture during magmatic intrusion and small relative displacements during the passage of seismic waves from distant earthquakes may damage structures built across them. The risk of structural damage may most likely be reduced considerably by avoiding building structures across the fractures. We suggest a change in building practice in fractures areas to achieve that.

Harmonic Oscillations of Nonlinear Two-Degree-of-Freedom Systems

1955 ◽  
Vol 22 (1) ◽  
pp. 107-110
Author(s):  
T. C. Huang
Keyword(s):  
Nonlinear System ◽  
Degrees Of Freedom ◽  
Forced Oscillations ◽  
Viscous Damping ◽  
Free Oscillations ◽  
Response Curves ◽  
Harmonic Oscillations ◽  
Restoring Force ◽  
Nonlinear Restoring Force ◽  
Two Degree Of Freedom

Abstract In this paper an investigation is made of equations governing the oscillations of a nonlinear system in two degrees of freedom. Analyses of harmonic oscillations are illustrated for the cases of (1) the forced oscillations with nonlinear restoring force, damping neglected; (2) the free oscillations with nonlinear restoring force, damping neglected; and (3) the forced oscillations with nonlinear restoring force, small viscous damping considered. Amplitudes of oscillations and frequency equations are derived based on the mathematically justified perturbation method. Response curves are then plotted.

Sign in / Sign up

Export Citation Format

Share Document