An Introduction to Random Vibrations, Spectral and Wavelet Analysis

Peppin, Richard J.

doi:10.1155/1994/561605

“…In literature, among the frequently used techniques for pre-processing (denoising) and extracting relevant features from such signals (data sets) is to decompose the signals into transient features. Over the years, techniques such as Wigner-Ville Distribution (WVD) (Wigner 1932), Short-Time Fourier Transform (STFT) (Peppin 1994;Newland 2005), Wavelet Transform (WT) (Daubechies 1989) and Empirical Mode Decomposition (EMD) (Huang et al 1998) have been employed for extracting transient features from nonlinear and nonstationary signals. However, studies have shown that these methods have some limitations.…”

Section: 1mentioning

confidence: 99%

“…The motivation for creating the hybrid is that, for ICEEMDAN, it has the ability to decompose nonlinear and nonstationary signals arising from complex systems into a series of Intrinsic Mode Functions (IMFs), where each resulting IMF represents the respective local transient features (Colominas et al 2014). Besides, when compared to existing filtering techniques for extracting transient features from nonlinear and nonstationary signals such as the Wigner-Ville Distribution (WVD) (Wigner 1932), Short-Time Fourier Transform (STFT) (Peppin 1994;Newland 2005), Wavelet Transform (WT) (Daubechies 1989) and Empirical Mode Decomposition (EMD) (Huang et al 1998), the ICEEMDAN drastically reduces the contamination of noise in a signal and the issue of mode mixing. In so doing, the inability to separate different frequencies into separate IMF's has been greatly resolved.…”

Section: Introductionmentioning

confidence: 99%

Hybrid intelligent predictive maintenance model for multiclass fault classification

Buabeng

¹

,

Simons

²

,

Frempong

³

et al. 2023

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Data recorded from monitoring the health condition of industrial equipment are often high-dimensional, nonlinear, nonstationary and characterised by high levels of uncertainty. These factors limit the efficiency of machine learning techniques to produce desirable results when developing effective fault classification frameworks. This paper sought to propose a hybrid artificial intelligent predictive maintenance model based on Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN), Principal Component Analysis (PCA) and Least Squares Support Vector Machine (LSSVM) optimised by the combination of Coupled Simulated Annealing and Nelder-Mead Simplex optimisation algorithms (ICEEMDAN-PCA-LSSVM). Here, ICEEMDAN was first employed as a denoising technique to decompose signals into series of Intrinsic Mode Functions (IMFs) of which only relevant IMFs containing the relevant fault features were retained for signal reconstruction. PCA was then employed as a dimension reduction technique through which the resulting set of uncorrelated features extracted served as input for LSSVM for classifying various fault types. The proposed technique is compared with three established methods (Linear Discriminant Analysis (LDA), Support Vector Machine (SVM) and Artificial Neural Network (ANN)) with multiclass classification capabilities. The various techniques were tested on an experimental UCI machine learning benchmark data obtained from multi-sensors of a hydraulic test rig. The results from the analysis revealed that the proposed ICEEMDAN-PCA-LSSVM technique is versatile and outperformed all the compared classifiers in terms of accuracy, error rate and other evaluation metrics considered. The proposed hybrid technique drastically reduced the redundancies and the dimension of features, allowing for the efficient consideration of relevant features for the enhancement of classification accuracy and convergence speed.

show abstract

“…In literature, among the frequently used techniques for pre-processing (denoising) and extracting relevant features from such signals (data sets) is to decompose the signals into transient features. Over the years, techniques such as Wigner-Ville Distribution (WVD) (Wigner 1932), Short-Time Fourier Transform (STFT) (Peppin 1994;Newland 2005), Wavelet Transform (WT) (Daubechies 1989) and Empirical Mode Decomposition (EMD) (Huang et al 1998) have been employed for extracting transient features from nonlinear and nonstationary signals. However, studies have shown that these methods have some limitations.…”

Section: 1mentioning

confidence: 99%

“…The motivation for creating the hybrid is that, for ICEEMDAN, it has the ability to decompose nonlinear and nonstationary signals arising from complex systems into a series of Intrinsic Mode Functions (IMFs), where each resulting IMF represents the respective local transient features (Colominas et al 2014). Besides, when compared to existing filtering techniques for extracting transient features from nonlinear and nonstationary signals such as the Wigner-Ville Distribution (WVD) (Wigner 1932), Short-Time Fourier Transform (STFT) (Peppin 1994;Newland 2005), Wavelet Transform (WT) (Daubechies 1989) and Empirical Mode Decomposition (EMD) (Huang et al 1998), the ICEEMDAN drastically reduces the contamination of noise in a signal and the issue of mode mixing. In so doing, the inability to separate different frequencies into separate IMF's has been greatly resolved.…”

Section: Introductionmentioning

confidence: 99%

Hybrid Intelligent Predictive Maintenance Model for Multiclass Fault Classification

Buabeng

¹

,

Simons

²

,

Frimpong

³

et al. 2021

Preprint

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Data recorded from monitoring the health condition of industrial equipment are often high-dimensional, nonlinear, nonstationary and characterised by high levels of uncertainty. These factors limit the efficiency of machine learning techniques to produce desirable results when developing effective fault classification frameworks. This paper sought to propose a hybrid artificial intelligent predictive maintenance model based on Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN), Principal Component Analysis (PCA) and Least Squares Support Vector Machine (LSSVM) optimised by the combination of Coupled Simulated Annealing and Nelder-Mead Simplex optimisation algorithms (ICEEMDAN-PCA-LSSVM). Here, ICEEMDAN was first employed as a denoising technique to decompose signals into series of Intrinsic Mode Functions (IMFs) of which only relevant IMFs containing the relevant fault features were retained for signal reconstruction. PCA was then employed as a dimension reduction technique through which the resulting set of uncorrelated features extracted served as input for LSSVM for classifying various fault types. The proposed technique is compared with three established methods (Linear Discriminant Analysis (LDA), Support Vector Machine (SVM) and Artificial Neural Network (ANN)) with multiclass classification capabilities. The various techniques were tested on an experimental UCI machine learning benchmark data obtained from multi-sensors of a hydraulic test rig. The results from the analysis revealed that the proposed ICEEMDAN-PCA-LSSVM technique is versatile and outperformed all the compared classifiers in terms of accuracy, error rate and other evaluation metrics considered. The proposed hybrid technique drastically reduced the redundancies and the dimension of features, allowing for the efficient consideration of relevant features for the enhancement of classification accuracy and convergence speed.

show abstract

“…The crossing statistics was first introduced by (Rice 1944). Since then, it has been used to study the geometry of stochastic fields in various disciplines, e.g., in complex systems (Brill 2000;Peppin 1994;Jafari et al 2006;Vahabi et al 2011), material sciences (Nezhadhaghighi et al 2017), optics (Goodman 2007;Yura & Hanson 2010;Pirlar et al 2017) and cosmology and early universe (Ryden et al 1989;Ryden 1988;Matsubara 1996;Movahed & Khosravi 2011;Matsubara 2003;Musso & Sheth 2014a,b). Crossing statistics can be introduced for 1, 2 and 3D stochastic fields.…”

Section: -The Unweighted Tpcf Of Up-crossingsmentioning

confidence: 99%

Multi-Scale Pipeline for the Search of String-Induced CMB Anisotropies

Sadr,

Movahed,

Farhang

et al. 2017

Preprint

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We propose a multi-scale edge-detection algorithm to search for the Gott-Kaiser-Stebbins imprints of a cosmic string (CS) network on the Cosmic Microwave Background (CMB) anisotropies. Curvelet decomposition and extended Canny algorithm are used to enhance the string detectability. Various statistical tools are then applied to quantify the deviation of CMB maps having a cosmic string contribution with respect to pure Gaussian anisotropies of inflationary origin. These statistical measures include the one-point probability density function, the weighted two-point correlation function (TPCF) of the anisotropies, the unweighted TPCF of the peaks and of the up-crossing map, as well as their cross-correlation. We use this algorithm on a hundred of simulated Nambu-Goto CMB flat sky maps, covering approximately 10% of the sky, and for different string tensions Gµ. On noiseless sky maps with an angular resolution of 0.9 , we show that our pipeline detects CSs with Gµ as low as Gµ 4.3 × 10 −10 . At the same resolution, but with a noise level typical to a CMB-S4 phase II experiment, the detection threshold would be to Gµ 1.2 × 10 −7 .

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An Introduction to Random Vibrations, Spectral and Wavelet Analysis

Cited by 7 publications

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Hybrid intelligent predictive maintenance model for multiclass fault classification

Hybrid intelligent predictive maintenance model for multiclass fault classification

Hybrid Intelligent Predictive Maintenance Model for Multiclass Fault Classification

Multi-Scale Pipeline for the Search of String-Induced CMB Anisotropies

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