Robust Damage Detection and Localization Under Complex Environmental Conditions Using Singular Value Decomposition-based Feature Extraction and One-dimensional Convolutional Neural Network

Ultrasonic guided wave is an attractive monitoring technique for large-scale structures but is vulnerable to changes in environmental and operational conditions(EOC),which are inevitable in the normal inspection of civil and mechanical structures.This paper thus presents a robust guided wave-based method for damage detection and localization under complex environmental conditions by singular value decomposition-based feature extraction and one-dimensional convolutional neural network(1D-CNN).After singular value decomposition-based feature extraction processing,a temporal robust damage index(TRDI)is extracted,and the effect of EOCs is well removed.Hence,even for the signals with a very large temperature-varying range and low signal-to-noise ratios(SNRs),the final damage detection and localization accuracy retain perfect 100%.Verifications are conducted on two different experimental datasets.The first dataset consists of guided wave signals collected from a thin aluminum plate with artificial noises,and the second is a publicly available experimental dataset of guided wave signals acquired on a composite plate with a temperature ranging from 20℃to 60℃.It is demonstrated that the proposed method can detect and localize the damage accurately and rapidly,showing great potential for application in complex and unknown EOC.

Contourlet watermarking algorithm based on Arnold scrambling and singular value decomposition

A new digital watermarking algorithm based on the contourlet transform is proposed to improve the robustness and anti-attack performances of digital watermarking. The algorithm uses the Arnold scrambling technique and the singular value decomposition （SVD） scheme. The Arnold scrambling technique is used to preprocess the watermark, and the SVD scheme is used to find the best suitable hiding points. After the contourlet transform of the carrier image, intermediate frequency sub-bands are decomposed to obtain the singularity values. Then the watermark bits scrambled in the Arnold rules are dispersedly embedded into the selected SVD points. Finally, the inverse contourlet transform is applied to obtain the carrier image with the watermark. In the extraction part, the watermark can be extracted by the semi-blind watermark extracting algorithm. Simulation results show that the proposed algorithm has better hiding and robustness performances than the traditional contourlet watermarking algorithm and the contourlet watermarking algorithm with SVD. Meanwhile, it has good robustness performances when the embedded watermark is attacked by Gaussian noise, salt- and-pepper noise, multiplicative noise, image scaling and image cutting attacks, etc. while security is ensured.

The Singular Value Decomposition Analysis between Summer Precipitation in the Dongting Lake Region and the Global Sea Surface Temperature

By dint of the summer precipitation data from 21 stations in the Dongting Lake region during 1960-2008 and the sea surface temperature(SST) data from NOAA,the spatial and temporal distributions of summer precipitation and their correlations with SST are analyzed.The coupling relationship between the anomalous distribution in summer precipitation and the variation of SST has between studied with the Singular Value Decomposition(SVD) analysis.The increase or decrease of summer precipitation in the Dongting Lake region is closely associated with the SST anomalies in three key regions.The variation of SST in the three key regions has been proved to be a significant previous signal to anomaly of summer rainfall in Dongting region.

IMPROVED SINGULAR VALUE DECOMPOSITION TECHNIQUE FOR DETECTING AND EXTRACTING PERIODIC IMPULSE COMPONENT IN A VIBRATION SIGNAL

Vibration acceleration signals are often measured from case surface of arunning machine to monitor its condition. If the measured vibration signals display to have periodicimpulse components with a certain frequency, there may exist a corresponding local fault in themachine, and if further extracting the periodic impulse components from the vibration signals, theseverity of the local fault can be estimated and tracked. However, the signal-to-noise ratios (SNRs)of the vibration acceleration signals are often so small that the periodic impulse components aresubmersed in much background noises and other components, and it is difficult or inconvenient for usto detect and extract the periodic impulse components with the current common analyzing methods forvibration signals. Therefore, another technique, called singular value decomposition (SVD), istried to be introduced to solve the problem. First, the principle of detecting and extracting thesignal periodic components using singular value decomposition is summarized and discussed. Second,the infeasibility of the direct use of the existing SVD based detecting and extracting approach ispointed out. Third, the approach to construct the matrix for SVD from the signal series is improvedlargely, which is the key program to improve the SVD technique; Other associated improvement is alsoproposed. Finally, a simulating application example and a real-life application example ondetecting and extracting the periodic impulse components are given, which showed that the introducedand improved SVD technique is feasible.

A NOTE ON SINGULAR VALUE DECOMPOSITION FOR RADON TRANSFORM IN R^n

The singular value decomposition is derived when the Radon transform is restricted to functions which are square integrable on the unit ball in R-n with respect to the weight W-lambda(x). It fulfilles mainly by means of the projection-slice theorem. The range of the Radon transform is spanned by products of Gegenbauer polynomials and spherical harmonics. The inverse transform of the those basis functions are given. This immediately leads to an inversion formula by series expansion and range characterizations.

Recursive State-space Model Identification of Non-uniformly Sampled Systems Using Singular Value Decomposition

In this paper a recursive state-space model identification method is proposed for non-uniformly sampled systems in industrial applications. Two cases for measuring all states and only output(s) of such a system are considered for identification. In the case of state measurement, an identification algorithm based on the singular value decomposition(SVD) is developed to estimate the model parameter matrices by using the least-squares fitting. In the case of output measurement only, another identification algorithm is given by combining the SVD approach with a hierarchical identification strategy. An example is used to demonstrate the effectiveness of the proposed identification method.

An Intercomparison of Rules for Testing the Significance of Coupled Modes of Singular Value Decomposition Analysis

This paper clarifies the essence of the significance test of singular value decomposition analysis （SVD）, and investigates four rules for testing the significance of coupled modes of SVD, including parallel analysis, nonparametric bootstrap, random-phase test, and a new rule named modified parallel analysis. A numerical experiment is conducted to quantitatively compare the performance of the four rules in judging whether a coupled mode of SVD is significant as parameters such as the sample size, the number of grid points, and the signal-to-noise ratio vary. The results show that the four rules perform better with lower ratio of the number of grid points to sample size. Modified parallel analysis and nonparametric bootstrap perform best to abandon the spurious coupled modes, but the latter is better than the former to retain the significant coupled modes when the sample size is not much larger than the number of grid points. Parallel analysis and random-phase test are robust to abandon the spurious coupled modes only when either （1） the observations at the grid points are spatially uncorrelated, or （2） the coupled signal is very strong for parallel analysis and is not weak for random-phase test. The reasons affecting the accuracy of the test rules are discussed.

Analysis of heart rate variability based on singular value decomposition entropy

Assessing the dynamics of heart rate fluctuations can provide valuable information about heart status. In this study, regularity of heart rate variability （HRV） of heart failure patients and healthy persons using the concept of singular value decomposition entropy （SvdEn） is analyzed. SvdEn is calculated from the time series using normalized singular values. The advantage of this method is its simplicity and fast computation. It enables analysis of very short and non-stationary data sets. The results show that SvdEn of patients with congestive heart failure （CHF） shows a low value （SvdEn： 0.056±0.006, p 〈 0.01） which can be completely separated from healthy subjects. In addition, differences of SvdEn values between day and night are found for the healthy groups. SvdEn decreases with age. The lower the SvdEn values, the higher the risk of heart disease. Moreover, SvdEn is associated with the energy of heart rhythm. The results show that using SvdEn for discriminating HRV in different physiological states for clinical applications is feasible and simple.

Estimation of fracture density and orientation from azimuthal elastic impedance difference through singular value decomposition

Accurate estimation of fracture density and orientation is of great significance for seismic characterization of fractured reservoirs.Here,we propose a novel methodology to estimate fracture density and orientation from azimuthal elastic impedance(AEI)difference using singular value decomposition(SVD).Based on Hudson's model,we first derive the AEI equation containing fracture density in HTI media,and then obtain basis functions and singular values from the normalized AEI difference utilizing SVD.Analysis shows that the basis function changing with azimuth is related to fracture orientation,fracture density is the linearly weighted sum of singular values,and the first singular value contributes the most to fracture density.Thus,we develop an SVD-based fracture density and orientation inversion approach constrained by smooth prior elastic parameters.Synthetic example shows that fracture density and orientation can be stably estimated,and the correlation coefficient between the true value and the estimated fracture density is above 0.85 even when an S/N ratio of 2.Field data example shows that the estimated fracture orientation is consistent with the interpretation of image log data,and the estimated fracture density reliably indicates fractured gas-bearing reservoir,which could help to guide the exploration and development of fractured reservoirs.

Super-resolution reconstruction of synthetic-aperture radar image using adaptive-threshold singular value decomposition technique

A super-resolution reconstruction approach of （SVD） technique was presented, and its performance was radar image using an adaptive-threshold singular value decomposition analyzed, compared and assessed detailedly. First, radar imaging model and super-resolution reconstruction mechanism were outlined. Then, the adaptive-threshold SVD super-resolution algorithm, and its two key aspects, namely the determination method of point spread function （PSF） matrix T and the selection scheme of singular value threshold, were presented. Finally, the super-resolution algorithm was demonstrated successfully using the measured synthetic-aperture radar （SAR） images, and a Monte Carlo assessment was carried out to evaluate the performance of the algorithm by using the input/output signal-to-noise ratio （SNR）. Five versions of SVD algorithms, namely 1 ） using all singular values, 2） using the top 80% singular values, 3） using the top 50% singular values, 4） using the top 20% singular values and 5） using singular values s such that S2≥/max（s2）/rinsNR were tested. The experimental results indicate that when the singular value threshold is set as Smax/（rinSNR）1/2, the super-resolution algorithm provides a good compromise between too much noise and too much bias and has good reconstruction results.

Source-Generated Noise Suppression Using the Singular Value Decomposition

Source-generated noise, such as air, refracted, guided waves, near-surface multiples, and radial ground roll, is one of the most challenging problems in the land seismic method. The interference of the noise with reflection events often results in a distorted representation of the subsurface and gives rise to interpretation uncertainties. To suppress the noise, geophysicists have devised various techniques in both acquisition and processing stages. Conventional processing methods, such as high-pass, f - k and hyperbolic velocity filters, however, have certain disadvantages when handling actual seismic data. In this study, we present a new hybrid method combining singular value decomposition (SVD) with a special linear transformation of the common-shot gather. The method is aimed at effectively removing the noise while minimizing harm to the signal. As compared with other methods, the SVD-based one gives a denser approximation to source-generated noise before its subtraction from the seismic data, due to the use of more appropriate basis functions. The special transformation applied in advance to the data is intended to align the source-generated noise events horizontally and thus to benefit the subsequent SVD. The effectiveness of the method in suppressing source-generated noise is demonstrated with a synthetic data set. Emphasis is put on the comparison of the performance of the method with that of conventional f - k filtering.

Solutions to the generalized Sylvester matrixequations by a singular value decomposition

In this paper, solutions to the generalized Sylvester matrix equations AX -XF = BY and MXN -X = TY with A, M ∈ R^n×n, B, T ∈ Rn×r, F, N ∈ R^p×p and the matrices N, F being in companion form, are established by a singular value decomposition of a matrix with dimensions n × （n ＋ pr）. The algorithm proposed in this paper for the euqation AX - XF = BY does not require the controllability of matrix pair （A, B） and the restriction that A, F do not have common eigenvalues. Since singular value decomposition is adopted, the algorithm is numerically stable and may provide great convenience to the computation of the solution to these equations, and can perform important functions in many design problems in control systems theory.

Analytic decomposition and numerical procedure for solving the singular boundary value problem arising in viscous flows

An efficient analytical decomposition technique was presented for solving the singular nonlinear boundary value problem arising in viscous flow when the Crocco variable was introduced. The approximate analytical solution may be represented in terms of a rapid convergent power series with elegantly computable terms. The reliability and efficiency of the approximate solutions were verified by numerical ones in the literature. The approximate analytical solutions can be successfully applied to give the values of skin friction coefficient.

Audio Zero-Watermark Scheme Based on Discrete Cosine Transform-Discrete Wavelet TransformSingular Value Decomposition

Traditional watermark embedding schemes inevitably modify the data in a host audio signal and lead to the degradation of the host signal.In this paper,a novel audio zero-watermarking algorithm based on discrete wavelet transform(DWT),discrete cosine transform(DCT),and singular value decomposition(SVD) is presented.The watermark is registered by performing SVD on the coefficients generated through DWT and DCT to avoid data modification and host signal degradation.Simulation results show that the proposed zero-watermarking algorithm is strongly robust to common signal processing methods such as requantization,MP3 compression,resampling,addition of white Gaussian noise,and low-pass filtering.

A Robust Image Watermarking Scheme Using Z-Transform, Discrete Wavelet Transform and Bidiagonal Singular Value Decomposition

Watermarking is a widely used solution to the problems of authentication and copyright protection of digital media especially for images,videos,and audio data.Chaos is one of the emerging techniques adopted in image watermarking schemes due to its intrinsic cryptographic properties.This paper proposes a new chaotic hybrid watermarking method combining Discrete Wavelet Transform(DWT),Z-transform(ZT)and Bidiagonal Singular Value Decomposition(BSVD).The original image is decomposed into 3-level DWT,and then,ZT is applied on the HH3 and HL3 sub-bands.The watermark image is encrypted using Arnold Cat Map.BSVD for the watermark and transformed original image were computed,and the watermark was embedded by modifying singular values of the host image with the singular values of the watermark image.Robustness of the proposed scheme was examined using standard test images and assessed against common signal processing and geometric attacks.Experiments indicated that the proposed method is transparent and highly robust.

Detection and correction of level echo based on generalized S-transform and singular value decomposition

The echo of the material level is non-stationary and contains many singularities.The echo contains false echoes and noise,which affects the detection of the material level signals,resulting in low accuracy of material level measurement.A new method for detecting and correcting the material level signal is proposed,which is based on the generalized S-transform and singular value decomposition(GST-SVD).In this project,the change of material level is regarded as the low speed moving target.First,the generalized S-transform is performed on the echo signals.During the transformation process,the variation trend of window of the generalized S-transform is adjusted according to the frequency distribution characteristics of the material level echo signal,achieving the purpose of detecting the signal.Secondly,the SVD is used to reconstruct the time-frequency coefficient matrix.At last,the reconstructed time-frequency matrix performs an inverse transform.The experimental results show that the method can accurately detect the material level echo signal,and it can reserve the detailed characteristics of the signal while suppressing the noise,and reduce the false echo interference.Compared with other methods,the material level measurement error does not exceed 4.01%,and the material level measurement accuracy can reach 0.40%F.S.

Randomized Generalized Singular Value Decomposition

The generalized singular value decomposition(GSVD)of two matrices with the same number of columns is a very useful tool in many practical applications.However,the GSVD may suffer from heavy computational time and memory requirement when the scale of the matrices is quite large.In this paper,we use random projections to capture the most of the action of the matrices and propose randomized algorithms for computing a low-rank approximation of the GSVD.Serval error bounds of the approximation are also presented for the proposed randomized algorithms.Finally,some experimental results show that the proposed randomized algorithms can achieve a good accuracy with less computational cost and storage requirement.

On the Application of Adomian Decomposition Method to Special Equations in Physical Sciences

The current manuscript makes use of the prominent iterative procedure, called the Adomian Decomposition Method (ADM), to tackle some important special differential equations. The equations of curiosity in this study are the singular equations that arise in many physical science applications. Thus, through the application of the ADM, a generalized recursive scheme was successfully derived and further utilized to obtain closed-form solutions for the models under consideration. The method is, indeed, fascinating as respective exact analytical solutions are accurately acquired with only a small number of iterations.

The Multi-Fractal Singularity Value Decomposition and Its Application in Extraction of Gravity Anomaly Associated with Gold Mineralization in Tongshi Gold Field

Because of the complication of geological procedures,the recorded data have the feature of nonlinear.The multi-fractal singularity value decomposition (MSVD) was used to decomposed the gravity data.In this paper,the MSVD was utilized to extract the gravity anomaly associated with the gold mineralization in Tongshi gold field in the southwest of Shandong province.The results showed that the Tongshi complex with negative circular gravity anomaly is an important ore-controlling factor.And the positive ring gravity anomaly distributed

Steering laws analysis of SGCMGs based on singular value decomposition theory

The steering laws of single gimbal control moment gyros （SGCMGs） are analyzed and compared in this paper for a spacecraft attitude control system based on singular value decomposition （SVD） theory. The mechanism of steering laws escaping singularity, especially how the steering laws affect singularity of gimbal configuration and the output torque error, is studied using SVD theory. Performance of various steering laws are analyzed and compared quantitatively by simulation. The obtained results can be used as a reference for designers.