Singular Wavelet Research Articles

A Novel Customised Load Adaptive Framework for Induction Motor Fault Classification Utilising MFPT Bearing Dataset

This research presents a novel Customised Load Adaptive Framework (CLAF) for fault classification in Induction Motors (IMs), utilising the Machinery Fault Prevention Technology (MFPT) bearing dataset. CLAF represents a pioneering approach that extends traditional fault classification methodologies by accounting for load variations and dataset customisation. Through a meticulous two-phase process, it unveils load-dependent fault subclasses that have not been readily identified in traditional approaches. Additionally, new classes are created to accommodate the dataset’s unique characteristics. Phase 1 involves exploring load-dependent patterns in time and frequency domain features using one-way Analysis of Variance (ANOVA) ranking and validation via bagged tree classifiers. In Phase 2, CLAF is applied to identify mild, moderate, and severe load-dependent fault subclasses through optimal Continuous Wavelet Transform (CWT) selection through Wavelet Singular Entropy (WSE) and CWT energy analysis. The results are compelling, with a 96.3% classification accuracy achieved when employing a Wide Neural Network to classify proposed load-dependent fault subclasses. This underscores the practical value of CLAF in enhancing fault diagnosis in IMs and its future potential in advancing IM condition monitoring.

Identification Strategy Design with the Solution of Wavelet Singular Spectral Entropy Algorithm for the Aerodynamic System Instability

In order to effectively identify the signs of instability in the aerodynamic system of an axial compressor, a wavelet singular spectral entropy algorithm incorporated within the wavelet transform, singular value decomposition and information entropy is proposed to describe the distribution complexity of the spatial modalities in the flow field. This kind of identification design can accurately distinguish the boundary between the stable and unstable states of the internal flow field from the view of a dynamic system. On the basis of the information entropy algorithm, the wavelet singular spectral entropy algorithm is designed to integrate with the advantages of wavelet transform analysis on the time-frequency localization and singular value decomposition for signal processing and data mining together. So that the quantitative analysis of the definition of rebuilding a system image can be achieved by the solution of wavelet singular spectral entropy. This method can automatically extract the transient information of the space mode in the time-frequency domain. It effectively avoids the shortcoming that the feature extraction on spatial information cannot be accomplished from multiple angles with the single information entropy algorithm. In the data processing of instability signals under different speeds, the wavelet singular spectral entropy algorithm shows a greater advantage in the early warning for compressor stall. The result shows that the value of the wavelet singular spectral shows an obvious mutation when the aerodynamic system approaches the instability boundary. According to the threshold set, the identification hybrid algorithm can detect the stall precursor about 23~96 r in advance. Compared to the single information entropy algorithm, the hybrid wavelet singular spectral entropy algorithm is able to shift to an earlier precursor identification by about 11~82 r. This established hybrid identification algorithm accounts for the nonlinearity of the aerodynamic system, providing a new perspective for the nonlinear system instability identification.

A DCT Fractional Bit Replacement Based Dual Watermarking Algorithm for Image Authentication

Abstract: Watermarking is a process of embedding a message inside a digital signal like an image, video or text. It is used for several key reasons such as authenticity verification, ownership recognition and hidden communication. In this paper, we discuss about image watermarking, where secret messages are stored in images. Introduction: We propose a dual watermarking approach, which is based on Discrete Cosine Transform, Discrete Wavelet Transform and Singular Value Decomposition methods. This paper considers one watermark as robust and other water mark as fragile. Method: The robust watermark is embedded in Discrete Wavelet Transform- Singular Value Decomposition - domain and is used to transmit hidden messages. The fragile watermark is embedded in Discrete Cosine Transform domain and is used for verification of secret message of the robust watermark. The proposed algorithm is tested in the experimental results section and shows promising results against denoising, rotation, translation and cropping attacks. Result: The results show that the performance of the proposed algorithm in terms of mean squared error, structural similarity and peak signal to noise ratio is S4considerable as compared with the existing methods. Discussion: We present the comparison results with Himanshu et. al. in table 10, from which we can see that our method performs better with gaussian noise and rotational attack only lacking with Salt and Pepper noise. Fig. 7 and Fig. 8, in terms of resulting PSNR shows the variation of noise variance and degree of rotation. From the graphs it is evident that out method performs better against Gaussian and rotational attack. Conclusion: In this paper a dual watermarking method is proposed in which one watermark is fragile which is called as authentication watermark whereas the other watermark is robust and is called as the information watermark. The authentication watermark is embedded in the fractional part of DCT domain in the cover image and the information watermark is embedded in the diagonal vector of the LL sub-band.

Standard and singular wavelet analysis

The paper suggests that the use of classical wavelets may be auxiliary in the analysis of a periodic signal. This is because the intuitive interpretation of the wavelet transform is not obvious. It is proposed to consider the Fourier transform as the main tool in applied research of periodic signals. An example is provided to support this point of view. To isolate the periodic component of the signal, along with wavelet analysis, it is proposed to perform spectral analysis. To do this, pre-filtering is performed using singular wavelets. This approach can significantly complement classical wavelet analysis.

State Identification of Transformer Under DC Bias Based on Wavelet Singular Entropy

To identify the DC bias state of transformers, a DC bias state identification method of transformer based on wavelet singular entropy is proposed in this paper. The vibration principle of transformers under DC bias has been analyzed. By combining continuous wavelet transform, singular value decomposition, and information entropy, the analysis method of wavelet singular entropy is proposed. The vibration signal of the transformer before and after DC bias is transformed by continuous wavelet transform, and then the wavelet time-frequency diagram is compared and analyzed. Furthermore, the DC bias state of the transformer is identified by wavelet singular entropy of vibration signal. The wavelet singular entropy under different states is in different numerical ranges, and the wavelet singular entropy of vibration signal under DC bias is significantly greater than that under no DC bias. The wavelet singular entropy effectively reflects the DC bias state of transformers. Then the proposed method is applied to a 500 kV transformer and a 220 kV transformer in the China Southern Power Grid. The results show that the proposed method can accurately and effectively identify the DC bias state of transformers.

Isolation of a periodic component by singular wavelet decomposition

In this paper, we propose to use a discrete wavelet transform with a singular wavelet to isolate the periodic component from the signal. Traditionally, it is assumed that the validity condition must be met for a basic wavelet (the average value of the wavelet is zero). For singular wavelets, the validity condition is not met. As a singular wavelet, you can use the Delta-shaped functions, which are involved in the estimates of Parzen-Rosenblatt, Nadaraya-Watson. Using singular value of a wavelet is determined by the discrete wavelet transform. This transformation was studied earlier for the continuous case. Theoretical estimates of the convergence rate of the sum of wavelet transformations were obtained; various variants were proposed and a theoretical justification was given for the use of the singular wavelet method; sufficient conditions for uniform convergence of the sum of wavelet transformations were formulated. It is shown that the wavelet transform can be used to solve the problem of nonparametric approximation of the function. Singular wavelet decomposition is a new method and there are currently no examples of its application to solving applied problems. This paper analyzes the possibilities of the singular wavelet method. It is assumed that in some cases a slow and fast component can be distinguished from the signal, and this hypothesis is confirmed by the numerical solution of the real problem. A similar analysis is performed using a parametric regression equation, which allows you to select the periodic component of the signal. Comparison of the calculation results confirms that nonparametric approximation based on singular wavelets and the application of parametric regression can lead to similar results.

BER Analysis of SWT Based OFDM ON LTE

We proposed to use singular wavelet transform (SWT) in OFDM based LTE because the SWT based system does not require a cyclic prefix, so spectrum efficiency is increased. SWT is used to analyze signals by the coefficients of SWT in both time and frequency domain. In order to investigate the bit error rate performance a practical channel model is required. Many channel models are proposed to mimic a real world scenario. Out of which Stanford university interim (SUI) channel provides best results so we replaced AWGN channel with SUI channel. We investigated the performance of bit error rates of SWT based OFDM in LTE for different modulation techniques such as QPSK, 64 QAM, 128 QAM under SUI 3 Channel model using SWT based haar and db2 transform. BER is reduced by 2 times when compared to the existing system.

Local transformations with a singular wavelet

The paper considers a local wavelet transform with a singular basis wavelet. The problem of nonparametric approximation of a function is solved by the use of the sequence of local wavelet transforms. Traditionally believed that the wavelet should have an average equal to zero. Earlier, the author considered singular wavelets when the average value is not equal to zero. As an example, the delta-shaped functions, participated in the estimates of Parzen – Rosenblatt and Nadara – Watson, were used as a wavelet. Previously, a sequence of wavelet transforms for the entire numerical axis and finite interval was constructed for singular wavelets. The paper proposes a sequence of local wavelet transforms, a local wavelet transform is defined, the theorems that formulate the properties of a local wavelet transform are proved. To confirm the effectiveness of the algorithm an example of approximating the function by use of the sum of discrete local wavelet transforms is given.

Jump Detection and Noise Separation by a Singular Wavelet Method for Predictive Analytics of High-Frequency Data

High-frequency data is a big data in finance in which a large amount of intra-day transactions arriving irregularly in financial markets are recorded. Given the high frequency and irregularity, such data require efficient tools to filter out the noise (i.e. jumps) arising from the anomaly, irregularity, and heterogeneity of financial markets. In this article, we use a recurrently adaptive separation algorithm, which is based on the maximal overlap discrete wavelet transform (MODWT) and that can effectively: (1) identify the time-variant jumps, (2) extract the time-consistent patterns from the noise (jumps), and (3) denoise the marginal perturbations. In addition, the proposed algorithm enables reinforcement learning to optimize a multiple-criteria decision or convex programming when reconstructing the wavelet-denoised data. Using simulated data, we show the proposed approach can perform efficiently in comparison with other conventional methods documented in the literature. We also apply our method in an empirical study by using high-frequency data from the US stock market and confirm that the proposed method can significantly improve the accuracy of predictive analytics models for financial market returns.

A No-reference Blur Image Quality Assessment Algorithm Based on Wavelet Singular Value Decomposition

A simple and effective no reference blur image quality assessment algorithm based on wavelet high frequency singular value decomposition is proposed. As the different wavelet high frequency sub-bands in the same level are highly structural correlation, and the degree of correlation would be weaken as the degree of blur distortion strengthen. The proposed method decomposes the images by wavelet transform firstly. Then the singular value decomposition is used for different high frequency sub-bands to get their singular value vectors, which we used to represent their structural information. Thirdly the angles between different sub-bands singular value vectors are computed, which reflects their degree of correlation. Finally the sum of angles is used as the last objective assessment index. Compared to the traditional methods, the proposed algorithm is more efficient and practical as it does not need to train or create a reference image. Experimental results show its good effectiveness and performance on LIVE2, CSIQ and TID2013 databases.

A Hybrid Procedure for Structural Damage Identification in Beam-Like Structures Using Wavelet Analysis

There are significant changes in the dynamic responses of damaged structures in which the damage depth becomes influential. This fact enables the recognition of damages in structures from their dynamic response data. This paper aims to identify damage locations as well as quantification of damage extent utilizing a vibration-based method. In this work, a signal-based damage identification procedure using the information entropy of wavelet packet energy is employed to evaluate beam-like structures. Damage indices called singular wavelet packet entropy and relative wavelet packet entropy are proposed to identify the location and to quantify the structural damage. The method involves two steps: firstly, the singular value of wavelet packet entropy, which reveals the abnormality distribution of the energy in signal time-frequency domain and secondly, relative wavelet packet entropy that is an acceptable damage feature to examine damage location and quantitative evaluation of the extent of damages through the vibration signals. The effects of wavelet type and decomposition level on the detection of damage location are examined. Numerical and experimental results from four test beams are used to verify the viability of this method. Results show that the damage indices method has great potential in identification of location and depth of cut in a steel beam. The procedure can be used for health monitoring of other complex structures.

고장전류의 누적 에너지를 이용한 저압직류 배전계통의 고저항 지락고장 검출 알고리즘 개발

Recently, new Low Voltage DC (LVDC) power distribution systems have been constantly researched as uses of DC in end-user equipment are increased. As in conventional AC distribution system, High Impedance Fault (HIF) which may cause a failure of protective relay can occur in LVDC distribution system as well. It, however, is hard to be detected since change in magnitude of current due to the fault is too small to detect the fault by the protective relay using overcurrent element. In order to solve the problem, this paper presents an algorithm for detecting HIF using accumulated energy in LVDC distribution system. Wavelet Singular Value Decomposition (WSVD) is used to extract abnormal high frequency components from fault current and accumulated energy of high frequency components is considered as the element to detect the fault. LVDC distribution system including AC/DC and DC/DC converter is modeled to verify the proposed algorithm using ElectroMagnetic Transient Program (EMTP) software. Simulation results considering various conditions show that the proposed algorithm can be utilized to effectively detect HIF.

Development of Fault Detector for Series Arc Fault in Low Voltage DC Distribution System using Wavelet Singular Value Decomposition and State Diagram

It is well known that series arc faults in Low Voltage DC (LVDC) distribution system occur at unintended points of discontinuity within an electrical circuit. These faults can make circuit breakers not respond timely due to low fault current. It, therefore, is needed to detect the series fault for protecting circuits from electrical fires. This paper proposes a novel scheme to detect the series arc fault using Wavelet Singular Value Decomposition (WSVD) and state diagram. In this paper, the fault detector developed is designed by using three criterion factors based on the RMS value of Singular value of Approximation (SA), Sum of the absolute value of Detail (SD), and state diagram. LVDC distribution system including AC/DC and DC/DC converter is modeled to verify the proposed scheme using ElectroMagnetic Transient Program (EMTP) software. EMTP/MODELS is also utilized to implement the series arc model and WSVD. Simulation results according to various conditions clearly show the effectiveness of the proposed scheme.

Algorithm for Fault Detection and Classification Using Wavelet Singular Value Decomposition for Wide-Area Protection

An algorithm for fault detection and classification method for wide-area protection in Korean transmission systems is proposed. The modeling of 345-kV and 765-kV Korean power system transmission networks using the Electro Magnetic Transient Program - Restructured Version (EMTP-RV) is presented and the algorithm for fault detection and classification in transmission lines is developed. The proposed algorithm uses the Wavelet Transform (WT) and Singular Value Decomposition (SVD). The Singular value of Approximation coefficient (SA) and part Sum of Detail coefficient (SD) are introduced. The characteristics of the SA and SD at the fault conditions are analyzed and used in the algorithm for fault detection and classification. The validation of the proposed algorithm is verified by various simulation results.

Research on Digital Watermarking Algorithm Based on Discrete Wavelet Transform and Singular Value Decomposition

Digital watermarking technology has become an important means of integrity and respect for people's authenticity, as well as users of copyright and intellectual property security and other interests such as the protection of digital works. In this paper, we proposed a watermarking algorithm based on discrete wavelet transform (DWT) of image and singular valued composition (SVD). The original image is decomposed with DWT,the watermarking image is decomposed with SVD after chaotic scrambling,and then the singular values of watermarking are embedded into some coefficients of decomposed original image. In this algorithm, after decomposing the original host image into four bands, we apply the SVD to watermark image,and modify DWT coefficients of the host image with the singular values of the watermark image. The outstanding features of the proposed algorithm are that it provides larger watermarking capacity and is more robust than others.

Artificial Bee Colony-based satellite image contrast and brightness enhancement technique using DWT-SVD

In this article, a new contrast enhancement approach is presented for quality enhancement of low-contrast satellite images. The proposed technique is based on the Artificial Bee Colony (ABC) algorithm using Discrete Wavelet Transform and Singular Value Decomposition (DWT-SVD). The method employs the ABC technique to learn the parameters of the adaptive thresholding function required for optimum enhancement. In this approach, the input image is primarily decomposed into four sub-bands through DWT, and then each sub-band of DWT is optimized through the ABC algorithm. After that, a singular value matrix of the low–low thresholded sub-band image is estimated and, finally, the enhanced image is constructed by applying inverse DWT. The results obtained through this method reveal that the proposed methodology gives better performance in terms of peak signal-to-noise ratio (PSNR), mean square error (MSE), and mean and standard deviation as compared to General Histogram Equalization (GHE), Discrete Cosine Transform and Singular Value Decomposition (DCT-SVD), DWT-SVD, Particle Swarm Optimization (PSO), and modified versions of the PSO-based enhancement approach.

Hiding digital image watermarking in a sound signal using Wavelet Transform and Singular Value Decomposition

Hiding digital image watermarking in a sound signal using Wavelet Transform and Singular Value Decomposition

Wavelet Packets of Nonstationary Random Processes: Contributing Factors for Stationarity and Decorrelation

The paper addresses the analysis and interpretation of second order random processes by using the wavelet packet transform. It is shown that statistical properties of the wavelet packet coefficients are specific to the filtering sequences characterizing wavelet packet paths. These statistical properties also depend on the wavelet order and the form of the cumulants of the input random process. The analysis performed points out the wavelet packet paths for which stationarization, decorrelation and higher order dependency reduction are effective among the coefficients associated with these paths. This analysis also highlights the presence of singular wavelet packet paths: the paths such that stationarization does not occur and those for which dependency reduction is not expected through successive decompositions. The focus of the paper is on understanding the role played by the parameters that govern stationarization and dependency reduction in the wavelet packet domain. This is addressed with respect to semi-analytical cumulant expansions for modeling different types of nonstatonarity and correlation structures. The characterization obtained eases the interpretation of random signals and time series with respect to the statistical properties of their coefficients on the different wavelet packet paths.

Fault Detection and Classification in EHV Transmission Line Based on Wavelet Singular Entropy

A novel technique for fault detection and classification in the extremely high-voltage transmission line using the fault transients is proposed in this paper. The novel technique, called wavelet singular entropy (WSE), incorporates the advantages of the wavelet transform, singular value decomposition, and Shannon entropy. WSE is capable of being immune to the noise in the fault transient and not being affected by the transient magnitude so it can be used to extract features automatically from fault transients and express the fault features intuitively and quantitatively even in the case of high-noise and low-magnitude fault transients. The WSE-based fault detection is performed in this paper, which proves the availability and superiority of WSE technique in fault detection. A novel algorithm based on WSE is put forward for fault classification and it is verified to be effective and reliable under various fault conditions, such as fault type, fault inception time, fault resistance, and fault location. Therefore, the proposed WSE-based fault detection and classification is feasible and has great potential in practical applications.