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In this paper, the recently developed analytical mode decomposition with a constant or time-varying cutoff frequency is extended into the decomposition of a non-stationary discrete time sequence. The discretization of the signal and the selection of the cutoff frequency may cause the failure of low frequency component extraction. In this study, to eliminate the effects of the signal discretization, the one-step, two-step, and four-step low-pass filters with cutoff frequencies are proposed. Based on the theoretical derivation, the previous one-step low-pass filter is effective only when the cutoff frequency is not greater than a quarter of the sampling frequency and the maximum frequency of the signal not greater than a half of the sampling frequency. In this study, if the cutoff frequency is less than or equal to a quarter of the sampling frequency, a two-step low-pass filter is proposed to extract the low frequency component. If the cutoff frequency is greater than a quarter of the sampling frequency, a four-step low-pass filter with frequency shifting process is proposed. When the time-varying cutoff frequency is not always larger than or less than a quarter of the sampling frequency, a sufficient condition, which is the sampling frequency is greater than four times of the maximum frequency of the signal component, is provided in this study. Two numerical examples are used to validate the effectiveness of the proposed low-pass filters. Both the theoretic derivation and numerical simulations show that the proposed filters can analytical extract the discrete low frequency component with an appropriate cutoff frequency. [ABSTRACT FROM AUTHOR]

GLO:BW7/30dec22:nme7165-toc-0001.jpg PHOTO (COLOR): . gl The cover image is based on the Research Article I Analytical uncertainty quantification approach based on adaptive generalized co-Gaussian process model i by Hua-Ping Wan et al., https://doi.org/10.1002/nme.7102. [Extracted from the article]

Root piles constitute a new type of pile in which a series of prefabricated reinforced concrete roots are inserted into the surrounding soil to improve the bearing capacity of the pile foundation. To investigate the nonlinear behaviour of root piles under lateral loading, an extended beam on nonlinear Winkler foundation (BNWF) model incorporating the soil–root interactions is proposed in this paper. The proposed model is aimed at simultaneously describing the additional bearing capacity provided by roots and the nonlinear soil–root interactions for laterally loaded root piles. Lateral loading tests are conducted on two full–scale root piles to verify the applicability and reliability of the proposed model. It is demonstrated that the proposed model can describe the lateral behaviour of root piles with a reasonable calculation accuracy. Further parametric analyses are conducted to investigate the lateral bearing behaviour of the root piles. It is found that the root pile increases the lateral bearing capacity of the piles owing to the roots. Increasing the number or length of roots and locating them in shallow soil layers can improve the lateral bearing capacity of the root piles. The obtained results are useful for the design and application of root piles. [ABSTRACT FROM AUTHOR]

• The time–frequency representation of fractional Fourier transform is theoretically derived in term of the window. • The analytical ridge point and corresponding ridge line of fractional Fourier transform is defined and presented. • The fractional Fourier transform based instantaneous frequency identification algorithm is formulated. • The feasibility and effectiveness of proposed method is verified by numerical signal and experimental results. The fractional Fourier transform involving a rotation angle as an additional variable is capable to transform a signal to any fractional Fourier domain in between time and frequency domain. With insight into the important role of rotation angle and time–frequency projection of fractional Fourier transform, the time–frequency representation of fractional Fourier transform is in this paper theoretically derived in terms of the window. It is demonstrated that the fractional Fourier transform in time–frequency domain is an algorithm of classical Fourier transform combined the chirp window that is adaptive dilation and translation. The window parameter properties are investigated in details and compared with those of wavelet window. To realize the structural instantaneous frequency identification, the analytical ridge point and corresponding ridge line based on the time–frequency representation of fractional Fourier transform is defined and presented. The fractional Fourier transform based instantaneous frequency identification algorithm is established accordingly by extracting ridge line. The effectiveness of proposed method is verified by a numerical multi-component non-stationary signal, a three-story frame on the shaking table excited by non-stationary inputs with different signal-to-noise ratios and a cable experiment with the time-varying tensioned forces. The identified instantaneous frequency results are compared with those obtained from short-time Fourier transform and wavelet transform. Both numerical and experimental verifications have demonstrated that the proposed fractional Fourier transform based method is capable of identification of instantaneous frequencies involving non-stationary signals with a sound robustness to noise. The fractional Fourier transform can be an alternative tool to process the non-stationary signals in time–frequency domain. [ABSTRACT FROM AUTHOR]

The transmissibility based operational modal analysis (TOMA) has drawn great attention due to its insensitivity to the nature of external excitation. Different from conventional modal identification approaches working in the frequency domain, it opens up a new path to find the system poles by utilizing mode shape information. Recently, the power spectral density transmissibility (PSDT) driven peak picking (PP) approach was proposed by authors for large-scale linear engineering structures under a single operational loading condition. As a nonparametric method, however, the PSDT-driven PP approach identifies natural frequencies by just observing signal-based features subjectively without fitting a parametric model. An enhanced PSDT approach is proposed in this study. The system poles are identified by employing the least-squares complex frequency-domain (LSCF) estimator, following which the mode shapes are evaluated by utilizing singular value decomposition (SVD) technique for PSDT matrix. As a result, a stabilization diagram containing the information of frequency, damping ratio and mode shape can be constructed to separate the stable system poles. Furthermore, the asymptotic analysis is implemented to investigate the robustness of PSDT to noise effect. The presented approach is able to maintain the benefits of PSDT and at the same time leads to an improvement of the modal parameter estimation. It is computationally efficient, simple, stable and robust to noise. A numerical example subjected to ground motion and two structures tested in the field are employed to demonstrate the efficiency and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]