Box-Cox sparse measures: A new family of sparse measures constructed from kurtosis and negative entropy

Wang, Dong; Zhong, Jingjing; Li, Chuan; Peng, Zhike

doi:10.1016/j.ymssp.2021.107930

Cited by 77 publications

(22 citation statements)

References 16 publications

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“…. , x n ) ∈ R n with E(x i ) = µ and V ar(x i ) = σ 2 , we can use a statistical parameter known as kurtosis [20], defined by kt = E( x i −µ σ ) 4 , to quantify the peakedness of its distribution. The larger kurtosis value kt means the sharper peakedness, equivalently the sparser distribution.…”

Section: Sparse Feature Generationmentioning

confidence: 99%

Quantization: Is It Possible to Improve Classification?

Lu¹,

Chen²,

guo³

et al. 2023

Preprint

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<p> Large-scale classification poses great challenges to storage and computation. There are two major solutions to address the problem: data compression and quantization. In the paper, we study the method of first reducing data dimension by random projection and then quantizing the projections to ternary and binary codes, which has been widely applied in practice. Often, the extreme quantization would degrade the accuracy of classification due to high quantization errors. Interestingly, however, we observe that the quantization could result in performance improvement, rather than degradation, if the data for quantization are preprocessed by sparse transform. Also, the quantization gain could be obtained with the random projections of the data, if both the data and random projection matrices are sparse enough, such that the resulting projections remain sparse. The intriguing performance is verified and analyzed with extensive experiments.<br> </p>

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Section: Sparse Feature Generationmentioning

confidence: 99%

Quantization: Is It Possible to Improve Classification?

Lu¹,

Chen²,

guo³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…It can be seen that the FCF is in direct proportion to the rotating frequency, and the proportionality coefficient is known as the fault characteristic coefficient (FCC) which can be used to locate the bearing fault. One can also find that if the rotating speed and the bearing type are given, the FCFs can be calculated according to equations ( 13)- (15). Note that for the inner race fault and ball fault, there exist sideband frequencies around the FCFs in the bearing vibration responses, denoted by FCF ± f r and FCF ± FTF, respectively, where FTF is fundamental train frequency (i.e., cage speed) expressed as…”

Section: Bearing Fault Signal Modelmentioning

confidence: 99%

“…9 However, the spectral kurtosis is sensitive to random impulse and may not find correct frequency bands under strong interference. Hence, more robust indexes like envelope harmonic-to-noise ratio, 10 spectral negentropy, 11 Gini index, 12,13 and generalized sparse index 14,15 have been employed for impulse signal detection. It should be noted that the above methods often adopt a filter bank with a structure of 1/3-binary tree to realize the fast traversal of all the possible frequency bands.…”

Section: Introductionmentioning

confidence: 99%

Non-stationary harmonic summation: A novel method for rolling bearing fault diagnosis under variable speed conditions

Chen

Wang

et al. 2022

Structural Health Monitoring

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Fault diagnosis of rolling bearings under variable speed conditions is a challenging task since the vibration signal exhibits time-varying non-stationary characteristics and is usually contaminated by strong noise. Most of the current researches employ the adaptive filtering or signal decomposition methods to obtain the impulse signals caused by the bearing fault before feature extraction, which, however, are not capable of removing the in-band noise. To address this issue, a novel method called non-stationary harmonic summation (NHS) is proposed based on the fact that the repetitive impulses caused by the bearing fault consist of a series of equally-spaced harmonics in the frequency domain. Firstly, the harmonic characteristics are theoretically analyzed and the results show that the impulses contain non-stationary harmonics with a time-varying spacing frequency (i.e., the fault characteristic frequency) under variable speed conditions. Next, according to the harmonic characteristics, an efficient algorithm combining the parameterized demodulation with the adaptive chirp mode decomposition is developed to extract the non-stationary harmonics and then summate these harmonics to reconstruct the repetitive impulses for the fault feature extraction. Since the NHS elaborately exploits the intrinsic harmonic structure of the impulse signals, the noise can be fully removed and the reconstructed signal is free of side-band interference caused by complex amplitude modulation. Both simulated and experimental signals are considered to demonstrate the advantages of the NHS for bearing fault diagnosis under variable speed conditions.

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“…In study 36 , spectral kurtosis, spectral NE, spectral GI and spectral smoothness index were found to fall into the sum of weighted normalized squared envelope (SWNSE) and the main difference among them is that different weight sequences are applied to the normalized squared envelope. Based on SWNSE and Box-Cox transformation, Box-Cox sparsity measures (BCSM) were proposed by Wang et al 37 as the generalization of kurtosis and NE for machine condition monitoring, and have been proved to satisfy six typical attributes of sparsity measures. The experimental results showed that BCSM can achieve the sparse quantization performance between kurtosis and NE by adjusting the transformation parameter 37,38 , which means that BCSM is also vulnerable to large random transients.…”

Section: Introductionmentioning

confidence: 99%

“…Based on SWNSE and Box-Cox transformation, Box-Cox sparsity measures (BCSM) were proposed by Wang et al 37 as the generalization of kurtosis and NE for machine condition monitoring, and have been proved to satisfy six typical attributes of sparsity measures. The experimental results showed that BCSM can achieve the sparse quantization performance between kurtosis and NE by adjusting the transformation parameter 37,38 , which means that BCSM is also vulnerable to large random transients. Chen et al 39 improved SWNSE for bearing condition monitoring by generalizing the norm order, but the construction of health indicators needs to meet strict parameter-setting requirements.…”

Section: Introductionmentioning

confidence: 99%

Power function-based Gini indices: New sparsity measures using power function-based quasi-arithmetic means for bearing condition monitoring

Chen

Zhang

et al. 2023

Structural Health Monitoring

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The Gini index (GI), GI II, and GI III are proven to be effective sparsity measures in the fields of machine condition monitoring and fault diagnosis, and they can be reformulated as the ratio of different quasi-arithmetic means (RQAM). Under this framework, generalized Gini indices (GGIs) have been developed for sparse quantification by applying nonlinear weights to GI, and another generalized form of GI, referred to here as power function-based Gini indices I (PFGI1s), has been introduced by using power function as the generator of quasi-arithmetic means. The GGIs with different weight parameters exhibit reliable sparse quantization capability for repetitive transient features, while their repetitive transient discriminability is lower than kurtosis and negentropy under noise contamination. PFGI1 achieves enhanced repetitive transient discriminability with increasing power exponent, showing the advantage of the generalization approach. In this paper, based on RQAM, a single-parameter generalization method for generating PFGI1s is introduced into GI II and GI III from the perspective of the quasi-arithmetic mean generator, which leads to the power function-based Gini indices II and III (PFGI2s and PFGI3s) constructed from GI II and GI III, respectively. Mathematical derivation proves that PFGI2s and PFGI3s satisfy at least five of six typical attributes of sparsity measures and are two new families of sparsity measures. Simulation analysis shows that, similar to PFGI1s, PFGI2s and PFGI3s can monotonically estimate the sparsity of the data sequence and can simultaneously achieve strong random transient resistibility and high repetitive transient discriminability compared with traditional sparsity measures. The experimental results of bearing run-to-failure demonstrate that PFGI1s, PFGI2s, and PFGI3s with appropriate power exponents can effectively quantify the repetitive transient features caused by bearing faults and can accurately characterize the bearing degradation status compared with the state-of-the-art sparsity measures.

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Box-Cox sparse measures: A new family of sparse measures constructed from kurtosis and negative entropy

Cited by 77 publications

References 16 publications

Quantization: Is It Possible to Improve Classification?

Quantization: Is It Possible to Improve Classification?

Non-stationary harmonic summation: A novel method for rolling bearing fault diagnosis under variable speed conditions

Power function-based Gini indices: New sparsity measures using power function-based quasi-arithmetic means for bearing condition monitoring

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