A method for detection and characterisation of structural non-linearities using the Hilbert transform and neural networks

Ondra, Václav; Sever, Ibrahim A.; Schwingshackl, Christoph W.

doi:10.1016/j.ymssp.2016.06.008

Cited by 33 publications

(22 citation statements)

References 14 publications

(29 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In recent decades, the impelling need to monitor and supervise machine and structures operations has led to an increasing usage of sensors and measuring equipment. Time varying data are analyzed and processed to obtain high fidelity models able to describe and ideally predict the system behavior under varying excitations and boundary conditions [1][2][3][4][5]. To this end, many strategies have been developed for system identifications generally based on linear theory, such as modal analysis [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of Governing Equations from Vibration Measurements for Geometrically Nonlinear Systems

et al. 2019

View full text Add to dashboard Cite

Data-driven system identification procedures have recently enabled the reconstruction of governing differential equations from vibration signal recordings. In this contribution, the sparse identification of nonlinear dynamics is applied to structural dynamics of a geometrically nonlinear system. First, the methodology is validated against the forced Duffing oscillator to evaluate its robustness against noise and limited data. Then, differential equations governing the dynamics of two weakly coupled cantilever beams with base excitation are reconstructed from experimental data. Results indicate the appealing abilities of data-driven system identification: underlying equations are successfully reconstructed and (non-)linear dynamic terms are identified for two experimental setups which are comprised of a quasi-linear system and a system with impacts to replicate a piecewise hardening behavior, as commonly observed in contacts.

show abstract

Section: Introductionmentioning

confidence: 99%

Reconstruction of Governing Equations from Vibration Measurements for Geometrically Nonlinear Systems

et al. 2019

View full text Add to dashboard Cite

show abstract

“…According to the characteristics of the stiffness and damping marginal curves mentioned in Section 2.2, a total of nine NFIs are proposed to describe the characteristics of the nonlinear models.…”

Section: Structural Dynamic Nonlinear Model Identificationmentioning

confidence: 99%

“…In general, the nonlinear system identification methods can be classified as time domain, frequency domain, and time–frequency domain methods. The restoring force surface (RFS), proposed by Masri and Caughey, is the representation of time domain method which initiated the analysis of nonlinear structural systems in terms of their internal RFSs. However, there are still several limitations in the RFS.…”

Section: Introductionmentioning

confidence: 99%

Structural dynamic nonlinear model and parameter identification based on the stiffness and damping marginal curves

Wang

Ding

Ren

et al. 2020

Struct Control Health Monit

View full text Add to dashboard Cite

Summary This paper presents a novel structural dynamic nonlinear model and parameter identification method based on the stiffness and damping marginal curves. The stiffness and damping marginal curves are first extracted from the structural dynamic responses. Then, nine nonlinear feature indices (NFIs) are defined based on the marginal curves to describe the characteristics of various nonlinear models. To reduce the dimension of NFIs and facilitate the subsequent calculation of the support vector machine (SVM), the principal component analysis (PCA) is implemented. Afterwards, the NFIs processed by PCA are employed as the training samples to SVM classifier, which is used to identify the structural nonlinear model. According to the identified nonlinear model corresponding to the type of nonlinearity, the parameters of the nonlinear model are further identified by the nonlinear least square method. The numerical results of a single degree of freedom (SDOF) system and a cantilever beam structure demonstrate that the proposed method can effectively identify both nonlinear model and corresponding parameters under various excitations even considering the noise effect. Subsequently, the proposed method is also verified by a benchmark system subjected to a semisinusoidal pulse load and a beam bridge structure subjected to an earthquake load. The proposed method is also applied to the experimental test of a bolted joint cantilever beam subjected to a random excitation in the laboratory. Both numerical and test results demonstrate that the proposed method can identify both nonlinear model and corresponding parameters within good accuracy and robustness.

show abstract

“…1. Model identification, model validation and model updating for control and numerical simulation, mostly performed during the product development phase [1][2][3][4].…”

Section: Introductionmentioning

confidence: 99%

“…• advanced signal processing for updating gray-box models [1,2,4,8,9], • neural network based methods [10,11],…”

Section: Introductionmentioning

confidence: 99%

Recovery of Differential Equations from Impulse Response Time Series Data for Model Identification and Feature Extraction

2019

View full text Add to dashboard Cite

Time recordings of impulse-type oscillation responses are short and highly transient. These characteristics may complicate the usage of classical spectral signal processing techniques for (a) describing the dynamics and (b) deriving discriminative features from the data. However, common model identification and validation techniques mostly rely on steady-state recordings, characteristic spectral properties and non-transient behavior. In this work, a recent method, which allows reconstructing differential equations from time series data, is extended for higher degrees of automation. With special focus on short and strongly damped oscillations, an optimization procedure is proposed that fine-tunes the reconstructed dynamical models with respect to model simplicity and error reduction. This framework is analyzed with particular focus on the amount of information available to the reconstruction, noise contamination and nonlinearities contained in the time series input. Using the example of a mechanical oscillator, we illustrate how the optimized reconstruction method can be used to identify a suitable model and how to extract features from uni-variate and multivariate time series recordings in an engineering-compliant environment. Moreover, the determined minimal models allow for identifying the qualitative nature of the underlying dynamical systems as well as testing for the degree and strength of nonlinearity. The reconstructed differential equations would then be potentially available for classical numerical studies, such as bifurcation analysis. These results represent a physically interpretable enhancement of data-driven modeling approaches in structural dynamics.

show abstract

A method for detection and characterisation of structural non-linearities using the Hilbert transform and neural networks

Cited by 33 publications

References 14 publications

Reconstruction of Governing Equations from Vibration Measurements for Geometrically Nonlinear Systems

Reconstruction of Governing Equations from Vibration Measurements for Geometrically Nonlinear Systems

Structural dynamic nonlinear model and parameter identification based on the stiffness and damping marginal curves

Recovery of Differential Equations from Impulse Response Time Series Data for Model Identification and Feature Extraction

Contact Info

Product

Resources

About