Capillary rogue waves

We report the first observation of extreme wave events (rogue waves) in parametrically driven capillary waves. Rogue waves are observed above a certain threshold in forcing. Above this threshold, frequency spectra broaden and develop exponential tails. For the first time we present evidence of strong four-wave coupling in non-linear waves (high tricoherence), which points to modulation instability as the main mechanism in rogue waves. The generation of rogue waves is identified as the onset of a distinct tail in the probability density function of the wave heights. Their probability is higher than expected from the measured wave background.Comment: 4 pages, 5 figure

The energy cascade of surface wave turbulence: toward identifying the active wave coupling

We investigate experimentally turbulence of surface gravity waves in the Coriolis facility in Grenoble by using both high sensitivity local probes and a time and space resolved stereoscopic reconstruction of the water surface. We show that the water deformation is made of the superposition of weakly nonlinear waves following the linear dispersion relation and of bound waves resulting from non resonant triadic interaction. Although the theory predicts a 4-wave resonant coupling supporting the presence of an inverse cascade of wave action, we do not observe such inverse cascade. We investigate 4-wave coupling by computing the tricoherence i.e. 4-wave correlations. We observed very weak values of the tricoherence at the frequencies excited on the linear dispersion relation that are consistent with the hypothesis of weak coupling underlying the weak turbulence theory.Comment: proceedings of the Euromech-Ercoftac workshop "Turbulent Cascades II" organized in Ecole Centrale de Lyon in december 201

Identifying nonlinear wave interactions in plasmas using two-point measurements: a case study of Short Large Amplitude Magnetic Structures (SLAMS)

A framework is described for estimating Linear growth rates and spectral energy transfers in turbulent wave-fields using two-point measurements. This approach, which is based on Volterra series, is applied to dual satellite data gathered in the vicinity of the Earth's bow shock, where Short Large Amplitude Magnetic Structures (SLAMS) supposedly play a leading role. The analysis attests the dynamic evolution of the SLAMS and reveals an energy cascade toward high-frequency waves.Comment: 26 pages, 13 figure

Detection of Nonlinear Behavior in Voltage Source Converter Control in Wind Farms Based on Higher-Order Spectral Analysis

In recent years, the sub-synchronous oscillation (SSO) accidents caused by wind power have received extensive attention. A method is needed to distinguish if nonlinear behavior exists in the recorded equal-amplitude accident waveforms, so that different methods can be adopted to analyze the mechanism of the oscillation. The theory of higher-order statistics (HOS) has become a powerful tool for detection of nonlinear behavior (DNB) in production quality control since 1960s. However, HOS analysis has been applied in mechanical condition monitoring and fault diagnosis, even after being introduced into the power system and wind farms. This paper focuses on the voltage source converter (VSC) control systems in wind farms and tries to detect the nonlinear behavior caused by the bilateral or unilateral saturation hard limits based on HOS analysis. First, the traditional describing function is extended to obtain more frequency domain information, and hereby the harmonic characteristics of bilateral and the unilateral saturation hard limit are studied. Then the bispectrum and trispectrum are introduced as HOS, which are extended into bicoherence and tricoherence spectrums to eliminate the effects from linear parts in the VSC control system. The effectiveness of DNB and classification based on HOS is strictly proved and its detailed calculation and estimation process is illustrated. Finally, the proposed method is demonstrated and further discussed through simulation results

The New Second and Higher Order Spectral Technique for Damage Monitoring of Structures and Machinery

The new second and higher order spectral technique, the cross-covariance of complex spectral components, is proposed for monitoring damage of structure and machinery Normalization of the proposed technique is also developed. It is shown by simulation that the proposed technique provides effectiveness gain for detecting of damage compared to the higher order spectra

Identifying higher-order interactions in wave time-series

Reliable design and reanalysis of coastal and offshore structures requires, amongst other things, characterisation of extreme crest elevation corresponding to long return periods, and of the evolution of a wave in space and time conditional on an extreme crest. Extreme crests typically correspond to focussed wave events enhanced by wave-wave interactions of different orders. Higher-order spectral analysis can be used to identify wave-wave interactions in time-series of water surface elevation. The bispectrum and its normalised form (the bicoherence) have been reported by numerous authors as a means to characterise three-wave interactions in laboratory, field and simulation experiments. The bispectrum corresponds to a frequency-domain representation of the third order cumulant of the time-series, and can be thought of as an extension of the power spectrum (itself the frequency-domain representation of the second order cumulant). The power spectrum and bispectrum can both be expressed in terms of the Fourier transforms of the original time-series. The Fast Fourier transform (FFT) therefore provides an efficient means of estimation. However, there are a number of important practical considerations to ensuring reasonable estimation. To detect four-wave interactions, we need to consider the trispectrum and its normalised form (the tricoherence). The trispectrum corresponds to a frequency-domain (Fourier) representation of the fourth-order cumulant of the time-series. Four-wave interactions between Fourier components can involve interactions of the type where f1 + f2 + f3 = f4 and where f1 + f2 = f3 + f4, resulting in two definitions of the trispectrum, depending on which of the two interactions is of interest. We consider both definitions in this paper. Both definitions can be estimated using the FFT, but it’s estimation is considerably more challenging than estimation of the bispectrum. Again, there are important practicalities to bear in mind. In this work, we consider the key practical steps required to correctly estimate the trispectrum and tricoherence. We demonstrate the usefulness of the trispectrum and tricoherence for identifying wave-wave interactions in synthetic (based on combinations of sinusoids and on the HOS model) and measured wave time-series

Physical insights, characteristics and diagnosis of structural freeplay nonlinearity in transonic aeroelastic systems: a system identification based approach

The Next Generation of aircraft sustainment is based on an emerging paradigm known as Prognostics and Health Management. PHM encompasses numerous innovative concepts which shape the future of air asset sustainment according to pre-emptive condition-based maintenance, intelligence-based individual aircraft tracking, and damage/fault prognosis. Smart Diagnostics is an integral component of the SPHM paradigm, and refers to the detection, localisation and tracking of nonlinear structural anomalies that occur in various forms across the airframe structure or within mechanical interfaces. Control surface damage/ failure scenarios, such as, nonlinear hinge stiffness, backlash, and structural freeplay, are a class of structural anomaly which plague modern aircraft and introduce a range of dangerous nonlinear dynamic behaviours, such as, chaotic response and limit cycle oscillation. As a result, the freeplay structural anomaly can reduce fatigue life and is problematic for the stakeholder on many levels, including the management of structural health, maintenance practices, asset availability, mission capability, and sustainment provisions. The traditional approach to handling freeplay-type nonlinear events is based on avoidance and pre-emptive repetitive maintenance practices which, despite being over-conservative, inefficient and expensive, have remained unchanged for more than half a century. As the aerospace sector begins to adopt modern aircraft design and sustainment practices, including the realisation of SPHM-based technologies, there is an urgent requirement for contemporary solutions towards the diagnosis and tracking of structural freeplay anomalies. The research presented in this thesis is pursued with the global objective of contributing towards contemporary structural health monitoring technology through a nonlinear system identification framework for rapid control surface freeplay diagnostics. The proposed framework is driven by the fundamental assumption that all information pertaining to the freeplay event is contained within the time-histories extracted from an aircraft¿s sensory network. It is shown that through careful adaptation of well-established nonlinear system identification methods, namely the Higher-Order Spectra (HOS) and Hilbert-Huang Transform (HHT), rapid detection, localisation and magnitude tracking of the freeplay event is realisable, through a truly data-driven framework, with no inherent dependency of knowledge of the airframe structure, the flight parameters, the aerodynamic condition, or uncertainties. A novel and systematic approach is used to characterise the freeplay event, where nonlinear aeroelastic predictions (numerical aeroelastic models of increasing complexity) are considered to study the isolated physical freeplay mechanism in a nonlinear system identification setting, to understand how its physical action on an aeroelastic system can be exploited for diagnostics purposes. The findings are adapted to formulate temporal and spectral characteristic signatures, then implemented as a basis for the data-driven diagnostics strategy. A flight test case study is used to show that the signature-based diagnostics framework which is formulated using numerical cases with well-defined parameters, remains valid when diagnosing freeplay in a real-world aircraft system. The freeplay is detected and isolated, then a single tuned algorithm is shown to efficiently track the freeplay magnitude over the course of three years with several maintenance/ repair cycles, using a sensor with significant spatial discrepancy to the freeplay source. It is shown that rapid actionable diagnostics information can be extracted with a high level of robustness, demonstrated and verified by making consistent predictions despite: i) a large deviation in Mach number and angle-of-attack (with high angle manoeuvres), ii) highly nonlinear aerodynamic conditions, iii) no knowledge of uncertainty bounds, iv) mixture between stationary nonstationary response, and iv) little information available pertaining to the aircraft structural properties or geometry (a single geometric vector is used). In developing the diagnostics framework, numerous freeplay induced nonlinear phenomena are revisited, providing a new understanding of the structural freeplay physical mechanism. Several freeplay-induced nonlinear phenomena are defined, quantified and related according to a consolidated underlying nonlinear mechanism, founded upon empirically derived correlations. In showing that data-driven signature-based diagnostics is feasible for freeplay, this research makes a significant contribution towards the fields of nonlinear system identification, applied nonlinear dynamics and aircraft structural health monitoring. This provides a clear pathway to extend this signature-based system identification diagnostics strategy to capture other discrete nonlinear mechanisms in aircraft systems, or any relevant mechanical systems across the engineering disciplines. Requirements and limiting aspects of the data-driven approach are thoroughly discussed, predominantly related to sensory network requirements, and recommendations on how to address the limitations and progress with this research are clearly outlined