Signatures Of Nonlinear Dynamics Research Articles

Vibration-based breathing crack identification using non-linear intermodulation components under noisy environment

Structural damages can result in non-linear dynamical signatures such as lower and higher order harmonics and signal modulation that can significantly enhance their detection. The conventional spectral analysis is used in most existing vibration-based damage diagnostic techniques to extract these damage-sensitive non-linear features. However, the major limitation of using spectral analysis is that the amplitudes of non-linear harmonics are highly sensitive to measurement noise and may mislead the damage diagnostic process. Keeping this in view, we present a new reference-free damage diagnostic technique for fatigue-breathing crack detection, localization and characterization using the cyclic spectral analysis-based technique. A new damage index based on spectral correlation exploiting the non-linear intermodulation in the response is proposed. The proposed cyclic spectral analysis-based diagnostics are highly immune to the measurement noise. Numerical and experimental simulation studies have been carried out by considering a beam with single and multiple breathing cracks, to test and verify the robustness and effectiveness of the proposed technique.

A novel vibration based breathing crack localization technique using a single sensor measurement

Abstract Structural damages such as a fatigue-breathing crack can result in nonlinear dynamical signatures that can significantly enhance their detection. Majority of the existing vibration based breathing crack diagnosis techniques demands rather a dense sensor network in order to detect, precisely locate the spatial location and characterize the breathing crack as the change in the dynamic characteristics of a structure with breathing crack is much smaller when compared to open cracks of the same magnitude. Further, the quality of identification improves with the increase in the number of sensors. In this paper, a novel vibration-based damage detection technique based on the zero strain energy nodes concept is proposed for the first time to identify the exact spatial location of the breathing crack using a single sensor measurement. Two different procedures based on sweep sine and harmonic excitation are outlined for breathing crack localization. Multi-level Singular Spectrum Analysis (M-SSA) is used in the present work to conclude about the presence of nonlinear behaviour of the structure and also for the identification of frequencies at which the cracked structure behaves linearly. Numerical and experimental investigations presented in this paper clearly establish that the proposed approach has the ability to identify single and as well as multiple breathing cracks present anywhere in the structure even with noise contaminated measurements.

A method for detecting damage-induced nonlinearity in structures using weighting function augmented curvature approach

Structural damages can result in nonlinear dynamical signatures that can significantly enhance their detection. In this article, we present a new method for identifying damage-induced nonlinearity using vibration response measurements. Among the various types of damages that induce nonlinearity, we focus on the breathing crack. We use the spatial curvature of Fourier power spectrum augmented with rectangular weighting function as a damage-sensitive feature for breathing crack identification. The proposed rectangular weighting function significantly enhances the resolution of superharmonics and intermodulation exhibited by the frequency domain response of the structure with breathing crack for breathing crack identification and characterization. The proposed algorithm is simple, does not involve any complex post-processing and also does not require any numerical model. Both numerical and experimental studies have been carried out to test and verify the proposed algorithm.

Damage type classification based on structures nonlinear dynamical signature

Structural damages result in nonlinear dynamical signatures that significantly help for their monitoring. A damage type classification approach is proposed here that is based on a parallel Hammerstein models representation of the structure estimated by means of the Exponential Sine Sweep Method. This estimation method has been here extended to take into account for input signal amplitude which was not the case before. On the basis of these estimated models, three amplitude dependent damage indexes are built: one that monitors the shift of the resonance frequency of the structure, another the ratio of nonlinear versus linear energy in the output signal, and a last one the ratio of the energy coming from odd nonlinearities to the energy coming from even nonlinearities in the output signal. The slopes of these amplitude-dependent DIs are then used as coordinates to place the damaged structure under study within a three-dimensional space. A single mass-spring-damper system is considered to illustrate the ability of this space to classify different types of damage. Four types of damage with different severities are simulated through different spring nonlinearities: bilinear stiffness, dead zone, saturation, and Coulomb friction. For all severities, the four types of damage are extremely well separated within the proposed three-dimensional space, thus highlighting its high potential for classification purposes.

Nonlinear structural damage detection based on cascade of Hammerstein models

Structural damages result in nonlinear dynamical signatures that can significantly enhance their detection. An original nonlinear damage detection approach is proposed that is based on a cascade of Hammerstein models representation of the structure. This model is estimated by means of the Exponential Sine Sweep Method from only one measurement. On the basis of this estimated model, the linear and nonlinear parts of the outputs are estimated, and two damage indexes (DIs) are proposed. The first DI is built as the ratio of the energy contained in the nonlinear part of an output versus the energy contained in its linear part. The second DI is the angle between the subspaces obtained from the nonlinear parts of two sets of outputs after a principal component analysis. The sensitivity of the proposed DIs to the presence of damages as well as their robustness to noise is assessed numerically on spring–mass–damper structures and experimentally on composite plates with surface-mounted PZT-elements. Results demonstrate the effectiveness of the proposed method to detect a damage in nonlinear structures and in the presence of noise.

Signatures of Nonlinear Dynamics in an Idealized Atmospheric Model

Abstract Signatures of nonlinear dynamics are analyzed by studying the phase-space tendencies of a global baroclinic, quasigeostrophic, three-level (QG3) model with topography. Nonlinear, stochastic, low-order prototypes of the full QG3 model are constructed in the phase space of this model’s empirical orthogonal functions using the empirical model reduction (EMR) approach. The phase-space tendencies of the EMR models closely match the full QG3 model’s tendencies. The component of these tendencies that is not linearly parameterizable is shown to be dominated by the interactions between “resolved” modes rather than by multiplicative “noise” associated with unresolved modes. The method of defining the leading resolved modes and the interactions between them plays a key role in understanding the nature of the QG3 model’s dynamics, whether linear or nonlinear, deterministic or stochastic.

Aging Process Modulates Nonlinear Dynamics in Liver Cell Metabolism

Regulatory dynamics of energy metabolism in living cells entails a coordinated response of multiple enzyme networks that operate under non-equilibrium conditions. Here we show that mitochondrial dysfunctions associated with the aging process significantly modify nonlinear dynamical signatures in free radical generation/removal, thereby altering energy metabolism in liver cells. We support our data with a plausible biochemical mechanism for modified bioenergetics that involves uncoupling protein-2 that is up-regulated in aged cells as an adaptive response to mitigate increased oxidative stress. Combining high spatial and temporal resolution imaging and bio-energetic measurements, our work provides experimental support to the hypothesis that mitochondria manifest nonlinear dynamical behavior for efficiently regulating energy metabolism in intact cells, and any partial or complete reduction in this behavior would contribute to organ dysfunctions including the aging process and other disease processes.