Principal features for nonstationary signals from moments of the singular value decomposition of Cohen–Posch (positive time‐frequency) distributions

Abstract Road profiles are typically characterized by their spectral content. It has been noted by several researches, however, that road profiles are generally nonstationary signals that contain significant irregularities such as potholes. Such signals are not well described in the spectral domain. The objective of this work is to describe road profiles in the spatial domain by developing a set of characteristic shapes onto which individual events can be cast. A set of analytical functions describing these shapes is also developed. In order to develop a set a characteristic shapes, more than a million events are investigated from a mixture of road types (from highways to gravel roads) and a variety of locations throughout the United States. A set of characteristic shapes is developed for each road type and location. Although the events were drawn from diverse samples, the resulting sets of characteristic shapes are nearly indistinguishable. This similarity allows a single set of characteristic shapes to describe events for a wide class of roads. Variations in these sets are discussed and used in deriving a set of orthogonal analytical functions that describe the characteristic shapes. Individual road events are then mapped onto this set of characteristic shapes. The implications of decomposing road events into these characteristic shapes are discussed.

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Study on the Thick-Walled Pipe Ultrasonic Signal Enhancement of Modified S-Transform and Singular Value Decomposition

Mathematical Problems in Engineering ◽

10.1155/2015/312620 ◽

2015 ◽

Vol 2015 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

Haichao Cai ◽

Chunguang Xu ◽

Shiyuan Zhou ◽

Hongjuan Yan ◽

Liu Yang

Keyword(s):

Singular Value Decomposition ◽

Singular Value ◽

Frequency Resolution ◽

Scanning System ◽

Frequency Noise ◽

Echo Signal ◽

Time Frequency ◽

S Transform ◽

Ultrasonic Flaw ◽

Value Decomposition

When detecting the ultrasonic flaw of thick-walled pipe, the flaw echo signals are often interrupted by scanning system frequency and background noise. In particular when the thick-walled pipe defect is small, echo signal amplitude is often drowned in noise signal and affects the extraction of defect signal and the position determination accuracy. This paper presents the modified S-transform domain singular value decomposition method for the analysis of ultrasonic flaw echo signals. By changing the scale rule of Gaussian window functions with S-transform to improve the time-frequency resolution. And the paper tries to decompose the singular value decomposition of time-frequency matrix after the S-transform to determine the singular entropy of effective echo signal and realize the adaptive filter. Experiments show that, using this method can not only remove high frequency noise but also remove the low frequency noise and improve the signal-to-noise ratio of echo signal.

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A Tacholess Order Tracking Method Based on Inverse Short Time Fourier Transform and Singular Value Decomposition for Bearing Fault Diagnosis

Sensors ◽

10.3390/s20236924 ◽

2020 ◽

Vol 20 (23) ◽

pp. 6924

Author(s):

Lang Xu ◽

Steven Chatterton ◽

Paolo Pennacchi ◽

Chang Liu

Keyword(s):

Fourier Transform ◽

Singular Value Decomposition ◽

Rotation Frequency ◽

Singular Value ◽

Target Component ◽

Short Time Fourier Transform ◽

Time Frequency ◽

Order Tracking ◽

Value Decomposition ◽

Short Time

Order tracking has been widely used to diagnose failures of variable speed rotating machines. The performance of the TOT (Time-Frequency Domain Tacholess Order Tracking) methods is based on the correct separation of the target component strictly related to the shaft rotation frequency. Currently, most of the methods have focused on obtaining the instantaneous frequency with accuracy. In this paper, a new TOT method has been proposed that combines the inverse short-time Fourier transform (ISTFT) with singular value decomposition (SVD). The target component closely related to the shaft rotation frequency is selected and filtered approximately in the time-frequency domain. Hence, the ISTFT is adopted to reverse the target component into the time domain. Next, SVD is used to refine the roughly filtered target component. Finally, the phase of the refined signal is extracted to resample the original signal. The performance of the method was tested using real vibration signals collected from a large-scale test rig of a high-speed train traction system.

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