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A method for non-parametric identification of systems with asymmetric non-linear restoring forces is proposed in this paper. The method, named the zero-crossing method for systems with asymmetric restoring forces (ZCA), is an extension of zero-crossing methods and allows identification of backbones, damping curves and restoring elastic and dissipative forces from a resonant decay response. The validity of the proposed method is firstly demonstrated on three simulated resonant decay responses of the systems with off-centre clearance, bilinear and quadratic stiffness. Then, the method is applied to experimental data from a micro-electro-mechanical resonator in order to quantify its non-linear damping and stiffness effects. Throughout the paper the proposed method is also compared with the Hilbert vibration decomposition to demonstrate that the ZCA yields more accurate results with much less effort. [ABSTRACT FROM AUTHOR]

This paper presents a method for detection and characterisation of structural non-linearities from a single frequency response function using the Hilbert transform in the frequency domain and artificial neural networks. A frequency response function is described based on its Hilbert transform using several common and newly introduced scalar parameters, termed non-linearity indexes, to create training data of the artificial neural network. This network is subsequently used to detect the existence of non-linearity and classify its type. The theoretical background of the method is given and its usage is demonstrated on different numerical test cases created by single degree of freedom non-linear systems and a lumped parameter multi degree of freedom system with a geometric non-linearity. The method is also applied to several experimentally measured frequency response functions obtained from a cantilever beam with a clearance non-linearity and an under-platform damper experimental rig with a complex friction contact interface. It is shown that the method is a fast and noise-robust means of detecting and characterising non-linear behaviour from a single frequency response function. [ABSTRACT FROM AUTHOR]

• Identification of complex non-linear modes using the Hilbert-Huang transform (HHT) is presented. • The ability of the HHT to identify the complex non-linear modes is numerically investigated. • The findings highlight that the HHT can detect and characterise, but not quantify, non-linear behaviour. • The estimation of complex non-linear modes is also demonstrated experimentally. Modal analysis is a well-established method for analysis of linear systems, but its extension to non-linear structures has proven to be much more problematic. Several competitive definitions of non-linear modes and a variety of experimental methods have been introduced. In this paper, the definition of complex non-linear modes (CNMs) of mechanical systems is adopted and the possibility of their identification from experimental free decay responses using the Hilbert-Huang transform (HHT) is explored. It is firstly discussed that since there are similarities in the definition of intrinsic mode functions obtained using the HHT and reduced order model of slow-flow dynamics based on the CNMs, there is a reason to believe that the HHT can indeed extract the CNMs. This paper, however, presents a new insight into the use of the Hilbert-Huang transform by showing that the amplitude-dependent frequency and damping extracted from a free decay response are only suitable for detection and characterisation of non-linearities, but they cannot be used to quantify the non-linear behaviour by fitting the CNMs even if a model of the system is known. The analytical proof of the HHT cannot be currently formulated due to a limited understanding of its empirical nature. Instead, this unconventional conclusion is supported by a series of numerical studies of conservative and non-conservative non-linear systems with a wide range of parameters. In all cases, a special care is taken to apply the basic HHT only on such signals for which mode separation is possible (no mode-mixing occurs). This eliminates the need for more sophisticated HHT versions and clearly demonstrates the inability of the HHT to extract CNMs even for the simplest cases. In addition to numerical studies, the identification of several non-linear modes is demonstrated experimentally using the free decay responses obtained from the ECL benchmark. It is shown that the HHT is able to successfully extract several non-linear modes whose character correspond to the numerical reference, but which cannot be used to quantify the system parameters due to conclusions made in this paper. The findings highlight that the ability of the HHT to quantify non-linear behaviour using non-linear modes extracted from free decay responses is severely limited, while detection and characterisation of non-linear behaviour in a non-parametric manner is feasible. [ABSTRACT FROM AUTHOR]

• Novel concept of investigating blade vibration on the basis of sensor waveforms. • Mitigation of the under-sampling problem with BTT. • Modeling of a capacitive sensor based on experimental waveform data. • Asynchronous and synchronous single-harmonic and multi-harmonic vibration studies. • Sensitivity study of the error susceptibility of the methodology. A novel concept of investigating blade vibration in turbomachinery is presented on the basis of Bla de Tip-Timing (BTT) and clearance s ensor wavefor m a nalysis methods (BLASMA), with which vibration parameters are determined by global optimization. It is shown that the modulation of the sensor output by blade vibration can offer additional information compared with under-sampled time-of-arrival (TOA) data from traditional BTT applications. The sensor data can not only improve the validity of statements on blade vibration but also lessen the dependence on contact-based strain gauges measurements to produce reference data. A study was conducted to evaluate the merit of sensor waveform analysis with regard to determining asynchronous and synchronous single-harmonic and multi-harmonic blade vibration parameters. At first, waveforms were recorded with capacitive sensors during an experiment conducted on a research compressor. The experimentally measured waveforms were afterwards replicated in a simulator for imitating passing events of rotating and vibrating blades along a single virtual capacitive sensor. Finally, vibration properties, such as amplitudes, frequencies, and phases, are extracted from these waveforms with the help of global optimization methods. An investigation into the error proneness of the methodology is attached. [ABSTRACT FROM AUTHOR]