Time-Varying Weighted Optimal Empirical Mode Decomposition Using Multiple Sets of Basis Functions

Kızılkaya, Aydın; Elbi, Mehmet Dogan

doi:10.1007/s00034-017-0501-1

Cited by 2 publications

(2 citation statements)

References 33 publications

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“…In (Weng and Barner, 2008), authors utilize a linear and a bidirectional weighting for the reconstruction of the denoised signal. Authors in (Kizilkaya and Elbi, 2017a, 2017b; Kizilkaya et al, 2016) developed an optimal signal reconstruction algorithm in which time-varying weights are determined for each of the oscillation modes.…”

Section: Introductionmentioning

confidence: 99%

Component-scaled signal reconstruction for enhanced noise filtration

Singh

Moore

2022

Journal of Vibration and Control

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This research introduces a procedure for signal denoising based on linear combinations of intrinsic mode functions (IMFs) extracted using empirical mode decomposition (EMD). The method, termed component-scaled signal reconstruction, employs the standard EMD algorithm, with no enhancements to decompose the signal into a set of IMFs. The problem of mode mixing is leveraged for noise removal by constructing an optimal linear combination of the potentially mixed IMFs. The optimal linear combination is determined using an optimization routine with an objective function that maximizes and minimizes the information and noise, respectively, in the denoised signal. The method is demonstrated by applying it to a computer-generated voice sample and the displacement response of a cantilever beam with local stiffness nonlinearity. In the first application, the noise is introduced into the sample manually by adding a Gaussian white-noise signal to the signal. In the second application, the response of the entire beam is filmed using two 1-megapixel cameras, and the three-dimensional displacement field is extracted using digital image correlation. The noise in this application arises entirely from the images captured. The proposed method is compared to existing EMD, ensemble EMD, and LMD based denoising approaches and is found to perform better.

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Section: Introductionmentioning

confidence: 99%

Component-scaled signal reconstruction for enhanced noise filtration

Singh

Moore

2022

Journal of Vibration and Control

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“…31 Lapin investigated a regularization method to identify the time-varying nonlinear systems by means of Chebyshev polynomials of the first kind. 32 Although these methods of expanding the time-varying parameters by using the wavelet models, [33][34][35] the known basis functions [36][37][38] and the different polynomials [39][40][41] can track rapidly or even sharply varying parameters, the basis functions mentioned among the above approaches need to be known and are hard to select. To overcome this roadblock, a modified least-squares algorithm with covariance resetting is proposed for linearly parametrized time-varying systems by constructing a local polynomial approximation model in a finite sufficiently small time interval.…”

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confidence: 99%

Parameter estimation for a class of time‐varying systems with the invariant matrix

Ding

2022

Intl J Robust & Nonlinear

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This article is concerned with the identification of time-varying systems. Differently from the conventional polynomial approximation approaches, the changing laws of the time-varying parameters are considered to build the identification model for the time-varying systems. Specifically, the concept of the invariant matrix is put forward to characterize the time-varying parameters and to establish the state-space model with regard to the system parameters. Then this article proposes a stacked state estimation algorithm to achieve the time-varying parameter estimation. Moreover, for the purpose of enhancing the computational efficiency, a detached state estimation algorithm is proposed by reducing the dimension of the state vector to reconstruct the state equation. Finally, a numerical simulation example is employed to demonstrate the effectiveness of the proposed algorithms.

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Time-Varying Weighted Optimal Empirical Mode Decomposition Using Multiple Sets of Basis Functions

Cited by 2 publications

References 33 publications

Component-scaled signal reconstruction for enhanced noise filtration

Component-scaled signal reconstruction for enhanced noise filtration

Parameter estimation for a class of time‐varying systems with the invariant matrix

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