### Abstract

Empirical mode decomposition (EMD) is a powerful technique for separating the transient responses of nonlinear and nonstationary systems into finite sets of nearly orthogonal components, called intrinsic mode functions (IMFs), which represent the dynamics on different characteristic time scales. However, a deficiency of EMD is the mixing of two or more components in a single IMF, which can drastically affect the physical meaning of the empirical decomposition results. In this paper, we present a new approached based on EMD, designated as wavelet-bounded empirical mode decomposition (WBEMD), which is a closed-loop, optimization-based solution to the problem of mode mixing. The optimization routine relies on maximizing the isolation of an IMF around a characteristic frequency. This isolation is measured by fitting a bounding function around the IMF in the frequency domain and computing the area under this function. It follows that a large (small) area corresponds to a poorly (well) separated IMF. An optimization routine is developed based on this result with the objective of minimizing the bounding-function area and with the masking signal parameters serving as free parameters, such that a well-separated IMF is extracted. As examples of application of WBEMD we apply the proposed method, first to a stationary, two-component signal, and then to the numerically simulated response of a cantilever beam with an essentially nonlinear end attachment. We find that WBEMD vastly improves upon EMD and that the extracted sets of IMFs provide insight into the underlying physics of the response of each system.

Language | English (US) |
---|---|

Pages | 14-29 |

Number of pages | 16 |

Journal | Mechanical Systems and Signal Processing |

Volume | 99 |

DOIs | |

State | Published - Jan 15 2018 |

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### Keywords

- Empirical mode decomposition
- Nonlinear analysis
- Wavelet transform

### ASJC Scopus subject areas

- Control and Systems Engineering
- Signal Processing
- Civil and Structural Engineering
- Aerospace Engineering
- Mechanical Engineering
- Computer Science Applications

### Cite this

*Mechanical Systems and Signal Processing*,

*99*, 14-29. DOI: 10.1016/j.ymssp.2017.06.005

**Wavelet-bounded empirical mode decomposition for measured time series analysis.** / Moore, Keegan J.; Kurt, Mehmet; Eriten, Melih; McFarland, D. Michael; Bergman, Lawrence A.; Vakakis, Alexander F.

Research output: Contribution to journal › Article

*Mechanical Systems and Signal Processing*, vol 99, pp. 14-29. DOI: 10.1016/j.ymssp.2017.06.005

}

TY - JOUR

T1 - Wavelet-bounded empirical mode decomposition for measured time series analysis

AU - Moore,Keegan J.

AU - Kurt,Mehmet

AU - Eriten,Melih

AU - McFarland,D. Michael

AU - Bergman,Lawrence A.

AU - Vakakis,Alexander F.

PY - 2018/1/15

Y1 - 2018/1/15

N2 - Empirical mode decomposition (EMD) is a powerful technique for separating the transient responses of nonlinear and nonstationary systems into finite sets of nearly orthogonal components, called intrinsic mode functions (IMFs), which represent the dynamics on different characteristic time scales. However, a deficiency of EMD is the mixing of two or more components in a single IMF, which can drastically affect the physical meaning of the empirical decomposition results. In this paper, we present a new approached based on EMD, designated as wavelet-bounded empirical mode decomposition (WBEMD), which is a closed-loop, optimization-based solution to the problem of mode mixing. The optimization routine relies on maximizing the isolation of an IMF around a characteristic frequency. This isolation is measured by fitting a bounding function around the IMF in the frequency domain and computing the area under this function. It follows that a large (small) area corresponds to a poorly (well) separated IMF. An optimization routine is developed based on this result with the objective of minimizing the bounding-function area and with the masking signal parameters serving as free parameters, such that a well-separated IMF is extracted. As examples of application of WBEMD we apply the proposed method, first to a stationary, two-component signal, and then to the numerically simulated response of a cantilever beam with an essentially nonlinear end attachment. We find that WBEMD vastly improves upon EMD and that the extracted sets of IMFs provide insight into the underlying physics of the response of each system.

AB - Empirical mode decomposition (EMD) is a powerful technique for separating the transient responses of nonlinear and nonstationary systems into finite sets of nearly orthogonal components, called intrinsic mode functions (IMFs), which represent the dynamics on different characteristic time scales. However, a deficiency of EMD is the mixing of two or more components in a single IMF, which can drastically affect the physical meaning of the empirical decomposition results. In this paper, we present a new approached based on EMD, designated as wavelet-bounded empirical mode decomposition (WBEMD), which is a closed-loop, optimization-based solution to the problem of mode mixing. The optimization routine relies on maximizing the isolation of an IMF around a characteristic frequency. This isolation is measured by fitting a bounding function around the IMF in the frequency domain and computing the area under this function. It follows that a large (small) area corresponds to a poorly (well) separated IMF. An optimization routine is developed based on this result with the objective of minimizing the bounding-function area and with the masking signal parameters serving as free parameters, such that a well-separated IMF is extracted. As examples of application of WBEMD we apply the proposed method, first to a stationary, two-component signal, and then to the numerically simulated response of a cantilever beam with an essentially nonlinear end attachment. We find that WBEMD vastly improves upon EMD and that the extracted sets of IMFs provide insight into the underlying physics of the response of each system.

KW - Empirical mode decomposition

KW - Nonlinear analysis

KW - Wavelet transform

UR - http://www.scopus.com/inward/record.url?scp=85026866632&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85026866632&partnerID=8YFLogxK

U2 - 10.1016/j.ymssp.2017.06.005

DO - 10.1016/j.ymssp.2017.06.005

M3 - Article

VL - 99

SP - 14

EP - 29

JO - Mechanical Systems and Signal Processing

T2 - Mechanical Systems and Signal Processing

JF - Mechanical Systems and Signal Processing

SN - 0888-3270

ER -