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.

Local Mass Addition and Data Fusion for Structural Damage Identification Using Approximate Models

2020 ◽  
Vol 20 (11) ◽  
pp. 2050124
Author(s):  
Jilin Hou ◽  
Zhenkun Li ◽  
Qingxia Zhang ◽  
Łukasz Jankowski ◽  
Haibin Zhang
Keyword(s):  
Data Fusion ◽  
Objective Function ◽  
Structural Damage ◽  
Damage Identification ◽  
Structural Parameters ◽  
Identification Accuracy ◽  
Fe Model ◽  
Local Damage ◽  
Approximate Models ◽  
Structural Damage Identification

In practical civil engineering, structural damage identification is difficult to implement due to the shortage of measured modal information and the influence of noise. Furthermore, typical damage identification methods generally rely on a precise Finite Element (FE) model of the monitored structure. Pointwise mass alterations of the structure can effectively improve the quantity and sensitivity of the measured data, while the data fusion methods can adequately utilize various kinds of data and identification results. This paper proposes a damage identification method that requires only approximate FE models and combines the advantages of pointwise mass additions and data fusion. First, an additional mass is placed at different positions throughout the structure to collect the dynamic response and obtain the corresponding modal information. The resulting relation between natural frequencies and the position of the added mass is sensitive to local damage, and it is thus utilized to form a new objective function based on the modal assurance criterion (MAC) and [Formula: see text]-based sparsity promotion. The proposed objective function is mostly insensitive to global structural parameters, but remains sensitive to local damage. Several approximate FE models are then established and separately used to identify the damage of the structure, and then the Dempster–Shafer method of data fusion is applied to fuse the results from all the approximate models. Finally, fractional data fusion is proposed to combine the results according to the parametric probability distribution of the approximate FE models, which allows the natural weight of each approximate model to be determined for the fusion process. Such an approach circumvents the need for a precise FE model, which is usually not easy to obtain in real application, and thus enhances the practical applicability of the proposed method, while maintaining the damage identification accuracy. The proposed approach is verified numerically and experimentally. Numerical simulations of a simply supported beam and a long-span bridge confirm that it can be used for damage identification, including a single damage and multiple damages, with a high accuracy. Finally, an experiment of a cantilever beam is successfully performed.

Nonlinear Restoring Force Identification of Strongly Nonlinear Structures by Displacement Measurement

2021 ◽  
pp. 1-29
Author(s):  
Qinghua Liu ◽  
Zehao Hou ◽  
Ying Zhang ◽  
Xingjian Jing ◽  
Gaëtan Kerschen ◽  
...  
Keyword(s):  
Energy Harvesting ◽  
Vibration Isolation ◽  
Displacement Measurement ◽  
Identification Accuracy ◽  
Geometrical Parameters ◽  
Nonlinear Structures ◽  
Restoring Force ◽  
Experimental Conditions ◽  
Strongly Nonlinear ◽  
Nonlinear Restoring Force

Abstract Strongly nonlinear structures have attracted a great deal of attention in energy harvesting and vibration isolation recently. However, it is challenging to accurately characterize the nonlinear restoring force using analytical modeling or cyclic loading tests in many realistic conditions due to the uncertainty of installation parameters or other constraints, including space size and dynamic disturbance. Therefore, a displacement-measurement restoring force surface identification approach is presented for obtaining the nonlinear restoring force. Widely known quasi-zero stiffness, bistable and tristable structures are designed in a cantilever-beam system with coupled rotatable magnets to illustrate the strongly nonlinear properties in the application of energy harvesting and vibration isolation. Based on the derived physical model of the designed strongly nonlinear structures, the displacement-measurement restoring force surface identification with a least-squares parameter fitting is proposed to obtain the parameters of the nonlinear restoring force. The comparison between the acceleration integration and displacement differentiation methods for describing the restoring force surface of strongly nonlinear structures is discussed. Besides, the influence of the noise level on identification accuracy is investigated. In experimental conditions, quasi-zero stiffness, bistable, and tristable nonlinear structures with various geometrical parameters are utilized to analyze the identified nonlinear restoring force curve and measured force-displacement trajectory. Finally, experimental results verify the effectiveness of the displacement-measurement restoring force surface method to obtain the nonlinear restoring force.

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 Ballistic Resistance of Honeycomb Sandwich Panels under In-Plane High-Velocity Impact

2013 ◽  
Vol 2013 ◽  
pp. 1-20 ◽  
Author(s):  
Chang Qi ◽  
Shu Yang ◽  
Dong Wang ◽  
Li-Jun Yang
Keyword(s):  
Structural Parameters ◽  
Sandwich Panels ◽  
Unit Cell ◽  
Dynamic Responses ◽  
Honeycomb Core ◽  
Ballistic Resistance ◽  
Honeycomb Sandwich ◽  
Aluminum Honeycomb ◽  
Parametric Studies ◽  
Nonmonotonic Effects

The dynamic responses of honeycomb sandwich panels (HSPs) subjected to in-plane projectile impact were studied by means of explicit nonlinear finite element simulations using LS-DYNA. The HSPs consisted of two identical aluminum alloy face-sheets and an aluminum honeycomb core featuring three types of unit cell configurations (regular, rectangular-shaped, and reentrant hexagons). The ballistic resistances of HSPs with the three core configurations were first analyzed. It was found that the HSP with the reentrant auxetic honeycomb core has the best ballistic resistance, due to the negative Poisson’s ratio effect of the core. Parametric studies were then carried out to clarify the influences of both macroscopic (face-sheet and core thicknesses, core relative density) and mesoscopic (unit cell angle and size) parameters on the ballistic responses of the auxetic HSPs. Numerical results show that the perforation resistant capabilities of the auxetic HSPs increase as the values of the macroscopic parameters increase. However, the mesoscopic parameters show nonmonotonic effects on the panels' ballistic capacities. The empirical equations for projectile residual velocities were formulated in terms of impact velocity and the structural parameters. It was also found that the blunter projectiles result in higher ballistic limits of the auxetic HSPs.

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.

scholarly journals Experimental validation of the proposed extended Kalman filter with unknown inputs algorithm based on data fusion

2019 ◽  
Vol 39 (4) ◽  
pp. 835-849 ◽  
Author(s):  
Jinshan Huang ◽  
Xianzhi Li ◽  
Xiongjun Yang ◽  
Zhupeng Zheng ◽  
Ying Lei
Keyword(s):  
Kalman Filter ◽  
Data Fusion ◽  
Extended Kalman Filter ◽  
Experimental Validation ◽  
Structural Parameters ◽  
Wide Band ◽  
Unknown Inputs ◽  
Filter Methods ◽  
Filter Approach ◽  
Shear Building

The extended Kalman filter is a useful tool in the research of structural health monitoring and vibration control. However, the traditional extended Kalman filter approach is only applicable when the information of external inputs to structures is available. In recent years, some improved extended Kalman filter methods applied with unknown inputs have been proposed. The authors have proposed an extended Kalman filter with unknown inputs based on data fusion of partially measured displacement and acceleration responses. Compared with previous approaches, the drifts in the estimated structural displacements and unknown external inputs can be avoided. The feasibility of proposed extended Kalman filter with unknown inputs has been demonstrated by some numerical simulation examples. However, experimental validation of the proposed extended Kalman filter with unknown inputs has not been conducted. In this paper, an experiment is conducted to validate the effectiveness of the proposed approach. A five-story shear building model subjected to an unknown external excitation of wide-band white noise is conducted. Moreover, the data fusion of partially measured strain and acceleration responses from the building is adopted as it is difficult to accurately measure structural displacement in practice. Identified results show that the recently proposed extended Kalman filter with unknown inputs can be applied to identify structural parameters, structural states, and the unknown inputs in real time.

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