On the application of discrete-time Volterra series for the damage detection problem in initially nonlinear systems

Nonlinearities in the dynamical behavior of mechanical systems can degrade the performance of damage detection features based on a linearity assumption. In this article, a discrete Volterra model is used to monitor the prediction error of a reference model representing the healthy structure. This kind of model can separate the linear and nonlinear components of the response of a system. This property of the model is used to compare the consequences of assuming a nonlinear model during the nonlinear regime of a magneto-elastic system. Hypothesis tests are then employed to detect variations in the statistical properties of the damage features. After these analyses, conclusions are made about the application of Volterra series in damage detection.

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A probabilistic formulation of the damage detection problem

10.2514/6.1996-1625 ◽

1996 ◽

Cited By ~ 1

Author(s):

Loukas Papadopoulos ◽

Ephrahim Garcia

Keyword(s):

Damage Detection ◽

Detection Problem ◽

Probabilistic Formulation

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Simulation-based site amplification model for shallow bedrock sites in Korea

Earthquake Spectra ◽

10.1177/8755293020981984 ◽

2021 ◽

pp. 875529302098198

Author(s):

Muhammad Aaqib ◽

Duhee Park ◽

Muhammad Bilal Adeel ◽

Youssef M A Hashash ◽

Okan Ilhan

Keyword(s):

Linear Models ◽

Site Response ◽

Site Amplification ◽

One Dimensional ◽

Nonlinear Component ◽

Nonlinear Site Response ◽

Simulation Based ◽

Linear And Nonlinear ◽

Input Motion ◽

Nonlinear Components

A new simulation-based site amplification model for shallow sites with thickness less than 30 m in Korea is developed. The site amplification model consists of linear and nonlinear components that are developed from one-dimensional linear and nonlinear site response analyses. A suite of measured shear wave velocity profiles is used to develop corresponding randomized profiles. A VS30 scaled linear amplification model and a model dependent on both VS30 and site period are developed. The proposed linear models compare well with the amplification equations developed for the western United States (WUS) at short periods but show a distinct curved bump between 0.1 and 0.5 s that corresponds to the range of site natural periods of shallow sites. The response at periods longer than 0.5 s is demonstrated to be lower than those of the WUS models. The functional form widely used in both WUS and central and eastern North America (CENA), for the nonlinear component of the site amplification model, is employed in this study. The slope of the proposed nonlinear component with respect to the input motion intensity is demonstrated to be higher than those of both the WUS and CENA models, particularly for soft sites with VS30 < 300 m/s and at periods shorter than 0.2 s. The nonlinear component deviates from the models for generic sites even at low ground motion intensities. The comparisons highlight the uniqueness of the amplification characteristics of shallow sites that a generic site amplification model is unable to capture.

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Multi-stage approach for structural damage detection problem using basis pursuit and particle swarm optimization

Journal of Sound and Vibration ◽

10.1016/j.jsv.2016.08.024 ◽

2016 ◽

Vol 384 ◽

pp. 210-226 ◽

Cited By ~ 23

Author(s):

Saleheh Gerist ◽

Mahmoud R. Maheri

Keyword(s):

Particle Swarm Optimization ◽

Damage Detection ◽

Structural Damage ◽

Particle Swarm ◽

Basis Pursuit ◽

Structural Damage Detection ◽

Detection Problem ◽

Swarm Optimization ◽

Multi Stage

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Linear and nonlinear components of human electroretinogram

Journal of Neurophysiology ◽

10.1152/jn.1984.51.5.952 ◽

1984 ◽

Vol 51 (5) ◽

pp. 952-967 ◽

Cited By ~ 56

Author(s):

C. L. Baker ◽

R. F. Hess

Keyword(s):

Steady State ◽

Spatial Frequency ◽

Step Response ◽

Linear Component ◽

Fast Wave ◽

Uniform Field ◽

Nonlinear Component ◽

Symmetric Component ◽

Linear And Nonlinear ◽

Nonlinear Components

We compared electroretinographic (ERG) responses to uniform-field and a variety of pattern stimuli using both transient and steady-state analyses. Evidence is provided that for all of these stimuli, the peak at high temporal frequencies in the steady-state response corresponds to the fast wave of the transient response and that the peak at low temporal frequencies corresponds to the slow wave of the step response. A variety of contrast-modulated grating stimuli were used to demonstrate that the fast, high-frequency response can be regarded as the sum of two components, an "odd-symmetric" component, which behaves linearly and is independent of spatial frequency, and an "even-symmetric" component, which behaves nonlinearly and has a band-pass spatial-frequency dependence. The prevailing distinction that is made between pattern and uniform-field ERGs is a consequence of the fact that the uniform-field ERG is dominated by the odd-symmetric (linear) component, whereas the so-called pattern (contrast reversal) ERG reveals the even-symmetric (nonlinear) component in isolation. Since a uniform field can also drive the nonlinear component, the present dichotomy ("luminance" versus "pattern") can be better understood in terms of the linear and nonlinear components of the response rather than in terms of the stimuli that produce them.

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On the detection of a nonlinear damage in an uncertain nonlinear beam using stochastic Volterra series

Structural Health Monitoring ◽

10.1177/1475921719876086 ◽

2019 ◽

Vol 19 (4) ◽

pp. 1137-1150 ◽

Cited By ~ 1

Author(s):

Luis GG Villani ◽

Samuel da Silva ◽

Americo Cunha ◽

Michael D Todd

Keyword(s):

Volterra Series ◽

Novelty Detection ◽

Nonlinear Behavior ◽

System Response ◽

Baseline Model ◽

Nonlinear Beam ◽

Stochastic Version ◽

Nonlinear Components ◽

Baseline State ◽

Data Variation

In the present work, two issues that can complicate a damage detection process are considered: the uncertainties and the intrinsically nonlinear behavior. To deal with these issues, a stochastic version of the Volterra series is proposed as a baseline model, and novelty detection is applied to distinguish the condition of the structure between a reference baseline state (presumed “healthy”) and damaged. The studied system exhibits nonlinear behavior even in the reference condition, and it is exposed to a type of damage that causes the structure to display a nonlinear behavior with a different nature than the initial one. In addition, the uncertainties associated with data variation are taken into account in the application of the methodology. The results confirm that the monitoring of nonlinear coefficients and nonlinear components of the system response enables the method to detect the presence of the damage earlier than the application of some linear-based metrics. Besides that, the stochastic treatment enables the specification of a probabilistic interval of confidence for the system response in an uncertain ambient, thus providing more robust and reliable forecasts.

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BEHAVIORAL MODELING OF RF POWER AMPLIFIERS USING MODIFIED VOLTERRA SERIES

Journal of Circuits System and Computers ◽

10.1142/s0218126609005113 ◽

2009 ◽

Vol 18 (02) ◽

pp. 351-359 ◽

Cited By ~ 1

Author(s):

ZHE JIN ◽

YANWEI ZHOU ◽

ZHIHUAN SONG

Keyword(s):

Data Storage ◽

Power Amplifiers ◽

Communication Systems ◽

Volterra Series ◽

Memory Effects ◽

Behavioral Modeling ◽

Recursive Least Squares ◽

Volterra Model ◽

Rf Power Amplifiers ◽

Identification Algorithm

There has been intensive research in memoryless nonlinear behavioral modeling of power amplifiers (PAs). But in broadband communication systems, memory effects of PAs can no longer be ignored and traditional memoryless model cannot accurately characterize the input-output relationship of PAs. In order to treat memory effects and reduce the complexity of general Volterra model, a new behavioral PA model based on modified Volterra series is proposed. Since the characteristics of power amplifiers change during transmission time, a recursive least squares algorithm with size-fixed observation matrices is developed to update the parameters of the PA model. This identification algorithm, which uses only the latest sample data to identify the parameters, can decrease computational complexity and data storage space needed for identification. Simulations are carried out to validate the performances of the proposed PA model and identification algorithm.

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Damage Detection in Composite Structures via Scanning Laser Doppler Vibrometry Using Linear and Nonlinear Ultrasonic Wave Features

10.1115/1.0004188v ◽

2021 ◽

Author(s):

Mingjing Cen ◽

Yanfeng Shen

Keyword(s):

Damage Detection ◽

Ultrasonic Wave ◽

Composite Structures ◽

Laser Doppler ◽

Scanning Laser ◽

Laser Doppler Vibrometry ◽

Nonlinear Ultrasonic ◽

Linear And Nonlinear

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Considerations for Practical Neural Network Application to a Damage Detection Problem

Damage Assessment of Structures VI - Key Engineering Materials ◽

10.4028/0-87849-976-8.151 ◽

2005 ◽

pp. 151-158

Author(s):

S.G. Pierce ◽

Keith Worden ◽

Graeme Manson

Keyword(s):

Neural Network ◽

Damage Detection ◽

Detection Problem ◽

Network Application

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Effect of Negative Stiffness Content on the Periodic Motion of Nonlinearly Coupled Oscillators

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4052287 ◽

2021 ◽

Vol 16 (11) ◽

Author(s):

Mohammad A. Al-Shudeifat

Keyword(s):

Coupled Oscillators ◽

Dynamical Behavior ◽

Negative Stiffness ◽

Nonlinear Frequency ◽

Nonlinear Stiffness ◽

Nonlinear Coupling ◽

Nonlinear Dynamical ◽

Wide Range ◽

Coupling Force ◽

Linear And Nonlinear

Abstract The linear and nonlinear stiffness coupling forces in dynamical oscillators are usually dominated by positive stiffness components. Therefore, plotting the resultant force in y-axis with respect to the change in displacement in x-axis results in an odd symmetry in the first and third quadrants of the xy-plane. However, the appearance of negative stiffness content in coupling elements between dynamical oscillators generates a force that can be dominated by an odd symmetry in the second and fourth quadrants. The underlying nonlinear dynamical behavior of systems employing this kind of force has not been well-studied in the literature. Accordingly, the considered system here is composed of two linear oscillators that are nonlinearly coupled by a force of which the negative stiffness content is dominant. Therefore, the underlying dynamical behavior of the considered system in physical and dimensionless forms is studied on the frequency-energy plots where many backbone curves of periodic solution have been obtained. It is found that within a wide range of nonlinear frequency levels, the nonlinear coupling force is dominated by a strong negative stiffness content at the obtained frequency-energy plots backbones.

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