Frequency Domain Analysis of Uncertain Time-Varying Discrete-Time Systems

In order to increase the performance of underwater target line spectrum extraction, an adaptive polarization filtering line spectrum extraction method is researched in the paper. By using of the polarization characteristics of underwater target signals, the polarization characteristics of underwater target line spectrum signal is analyzed via singular value decomposition (SVD) method in frequency domain. Firstly, the line spectrum signal is presented by the eigenimage corresponding to the maximum singular value to increase the signal-to-noise ratio (SNR) of the signal. Then the polarization parameters are extracted according to the polarization characteristics of the line spectrum signals. And the line spectrum signal is filtered by constructing the polarization filtering function. The simulation results show that the output SNR of the proposed method are larger than that of conventional FFT analysis method when the SNR of the signal is larger than -9dB, and the detection probability of the proposed method is 100% when the SNR of the signal is -1 dB, while the detection probability of the conventional FFT analysis method is 27.73%. It shows that the proposed method provides a new approach for underwater line spectrum signal extraction techniques.

In this paper, we discuss and investigate the impulsive synchronization of fractional-order discrete-time chaotic systems. The proposed method is based on the impulsive synchronization theory used in the integer-order case on the one hand and the mathematical analysis of the fractional-order discrete-time systems on the other hand. Sufficient conditions for the stability of synchronization error system are given, and application example with numerical simulations is illustrated in order to verify that the proposed method is applicable and effective. Furthermore, in order to validate the proposed synchronization approach, we have also provided the experimental implementation results using Arduino Mega boards.

SummaryThe problem of assuring the asymptotic stability of a pulse width modulation (PMW) control scheme is a classical topic in control engineering, where a continuous‐time control signal is approximated by a piecewise constant signal. This paper proposes a general framework that either shows the local asymptotic stability of the closed‐loop PWM system or proves the convergence of the state to an invariant set, which is the case in the presence of limit cycles. The proposed method is based on a piecewise affine representation of the closed‐loop system in discrete time, and it uses semidefinite programming both to find a Lyapunov‐like function and to determine an estimate of the region of attraction. This is an important feature since the desired continuous‐time control action at some instants may be larger than the magnitude of the PWM signals, leading to saturation of the applied control action, a well‐known source of performance degradation and even instability. Two academic examples of applications are shown, in the domain of spacecraft positioning control and electric direct current (DC) motor servoing.

We consider the analysis and synthesis of discrete-time networked control systems (NCSs), where the plant has additive uncertainty and the controller is updated with the sensor information at stochastic time intervals. It is shown that the problem is linked to H∞-control of linear discrete-time stochastic systems and a new small gain theorem is established. Based on this result, sufficient conditions are given for ensuring mean square stability of the NCS, and the genetic algorithm is utilised to design the controller of the NCS based on a linear matrix inequality technique. An illustrative example is given to demonstrate the effectiveness of our proposed method.

A novel approach to jointly optimized spatial prediction the choice of the subsequent transform in video and image compression.In this paper we improve the performance, reduce cost and high complexity .In proposed method we use the Singular value decomposition it is well known that the images, often used in variety of computer applications, are difficult to store and transmit.One possible solution to overcome this problem is to use a data compression technique where an image is viewed as a matrix and then the operations are performed on the matrix.In this paper, image compression is achieved by using singular value decomposition (SVD) technique on the image matrix.The advantage of using the SVD is the property of energy compaction and its ability to adapt to the local statistical variations of an image.Further, the SVD can be performed on any arbitrary, square, reversible and non reversible matrix of m x n size.In this paper, SVD is utilized to compress and reduce the storage space of an image.In addition, the paper investigates the effect of rank in SVD decomposition to measure the quality in terms of compression ratio and PSNR.

Another approach for generating reduced order discrete time system using composite method is being proposed. The proposed method is validated by considering a Linear Time Invariant Discrete System (LTIDS) having single input single output(SISO) of higher order being represented in frequency domain. Eigen Spectrum Analysis and Least Squares moment matching methods form the proposed composite method to obtain the reduced numerator and denominator polynomials. The suitability of the proposed method is judged by comparing the step, impulse responses of the original and reduced systems. The performances of the systems are measured in terms of Steady State Error (SSE). It is seen from the numerical examples that the results are quite competitive as compared to other methods thus justifying the applicability of the proposed method.

Ranking based collaborative filtering (CF) as opposed to the well-known memory based collaborative filtering has better performance in accommodating user preferences. However, ranking based collaborative filtering still suffers both sparsity and scalability issues. This work incorporates the Singular Value Decomposition (SVD) technique to reduce the user-item rating matrix dimension to solve the scalability and sparsity of many unrated items faced by ranking based collaborative filtering. From the evaluation, the proposed method acquires 4 times higher coverage but 33.3% lower F1-score compared to BordaRank method. The proposed method also gets 6 times higher F1-score and 17.8% higher coverage compared to pure SVD method. The running time of the proposed method shows that on lower neighborhood size, the proposed method gets the fastest and the best performance. Thus, incorporation of SVD to ranking based CF can be a good approach to overcome sparsity and scalability problems.

Subpixel translation estimation using phase correlation is a fundamental task for numerous applications in the remote sensing community. The major drawback of the existing subpixel phase correlation methods lies in their sensitivity to corruption, including aliasing and noise, as well as the poor performance in the case of practical remote sensing data. This paper presents a novel subpixel phase correlation method using singular value decomposition (SVD) and the unified random sample consensus (RANSAC) algorithm. In the proposed method, SVD theoretically converts the translation estimation problem to one dimensions for simplicity and efficiency, and the unified RANSAC algorithm acts as a robust estimator for the line fitting, in this case for the high accuracy, stability, and robustness. The proposed method integrates the advantages of Hoge's method and the RANSAC algorithm and avoids the corresponding shortfalls of the original phase correlation method based only on SVD. A pixel-to-pixel dense matching scheme on the basis of the proposed method is also developed for practical image registration. Experiments with both simulated and real data were carried out to test the proposed method. In the simulated case, the comparative results estimated from the generated synthetic image pairs indicate that the proposed method outperforms the other existing methods in the presence of both aliasing and noise, in both accuracy and robustness. Moreover, the pixel locking effect that commonly occurs in subpixel matching was also investigated. The degree of pixel locking effect was found to be significantly weakened by the proposed method, as compared with the original Hoge's method. In the real data case, experiments using different bands of ZY-3 multispectral sensor-corrected images demonstrate the promising performance and feasibility of the proposed method, which is able to identify seams of the image stitching between sub-charge-coupled device units.

An output‐only multiple‐crack localization method is proposed in this paper to detect and localize breathing cracks in a stepped rotor, which utilizes the crack‐induced local shape distortions in super‐harmonic characteristic deflection shapes (SCDSs). To minimize the noise effects on SCDSs and improve the accuracy of SCDS‐based crack localization, singular value decomposition is adopted to estimate the SCDS as the dominant singular vector of output power spectral density matrix at a super‐harmonic frequency. Then, in order to better reveal shape distortions in the SCDSs, an after‐treatment technique called gapped smoothing method is applied to derive a damage index. Numerical experiments are carried out to investigate the performance of the proposed method based on a two‐disc stepped rotor‐bearing system with breathing cracks established by the finite element method. Results show that the method is effective for single and multiple crack localization in stepped rotors and interference of steps can be excluded. Furthermore, the method is robust to noise. Influences of crack depths and rotating speeds are also investigated, and how to choose the rotating speed for better crack localization is discussed.

An approach based on the singular spectrum decomposition (SSD)-singular value decomposition (SVD) and frequency weight energy operator (FWEO) was proposed for early fault diagnosis of rolling bearings. Since the interference of heavy noise in the early stage of bearing fault, SSD could eliminate abundant noise, meanwhile adaptively decompose the nonlinear, non-stationary signals into multiple mono-components which had distinct physical meanings. Subsequently, SVD was adopted for de-noising in every mono-components because the noise was distributed throughout the frequency domain. In the following, signal reconstruction was performed based on the selected mono-components with de-noising. Finally, FWEO was employed for envelop analysis and the early fault diagnosis of the rolling bearing is realized. Two groups of experiment data concerning signals of early bearing fault were investigated to valid the effectiveness of the proposed method, and good fault identification effects were obtained.

This chapter explains the theory of Principal component analysis (PCA) in detail and presents practical implementation issues along with various application examples. It introduces the mathematical concepts behind PCA such as mean value, covariance, eigenvalues, and eigenvectors. The principal components are ordered in way that the principal components retain information in descending order. In many cases, PCA is implemented using the singular value decomposition (SVD) of the covariance matrix. The standard PCA algorithm can be extended to support nonlinear principal components using nonlinear kernels. SVD is an important tool for factorizing an arbitrary real or complex matrix, with many applications in various research areas, such as signal processing and statistics. PCA can also be performed without eigenanalysis. This can be achieved by using neural networks that can be trained to extract the principal components of the training set.

SummaryKnowing the Network Function (NF) pertaining to a certain input–output couple individuated inside a linear electrical network (LEN) is crucial, as it provides a synthetic and effective description of the input–output relationship and allows one to derive several key features of the subject system as well as to devise proper strategies to modify them.From a mathematical point of view, an NF may be expressed as the product of a real number, called the gain constant (GC), by a real rational function of the complex variables, whose numerator and denominator are called the zero polynomial (ZP) and the characteristic polynomial (CP), respectively, and may be obtained by calculating the determinants of proper matrices. However, when a design‐oriented symbolic hand analysis is needed, calculating the said polynomials in this manner may turn out to be tediously cumbersome; and above all, such a route may fail to illuminate the way that their coefficients depend on the circuit elements. The same may be said of numerical computer methods, which are suited to providing a global description of the NF in the frequency domain rather than analytical expressions of its coefficients. In this paper, a method is proposed that permits one to obtain the ZP without calculating any determinants. With respect to other methods that achieve the same goal, the present one does not require prior calculation of the CP or a nullator‐norator pair (NNP) to be compulsorily inserted in the subject circuit. Instead, it is based on applying the Andreani‐Mattisson extension (AME) of the Cochrun–Grabel algorithm (CGA) for the calculation of the CP to a circuit obtained from the assigned one by inserting in the latter a proper dependent source. The nature of such new circuit allows the worker to employ the classical tools of LEN theory so as to make the analysis as simple as possible and often performable by straightforward inspection, without the need for possibly involved equilibrium equations. Moreover, it is shown how the same technique can be applied to a properly modified version of the original network in order to calculate the CP as well. In this case (not compulsorily but if judged convenient for simplifying the calculations), a NNP may be employed in conjunction with the dependent source. The proposed method once again allows one to exploit the classic tools of LEN theory so as to considerably, if not drastically, simplify the analysis associated with the direct application of the AME to the original network. Finally, the calculation of the GC (that completes the knowledge of the whole NF under study) as well as circuit degeneracy are discussed and practical examples of application of the proposed techniques are given. Copyright © 2013 John Wiley & Sons, Ltd.

The signal-to-noise ratio (SNR) of nuclear magnetic resonance (NMR) logging signal is very low, and de-noising is an important factor for the validity of NMR logging method. A new method was proposed and applied in the filtering of NMR logging signal, based on the combination of generalized S transform and singular value decomposition (SVD). The basic theory and realization process of the combined method are given. The simulated and the measured data are analyzed and the results are compared with those of wavelet soft threshold method. Results show that the presented method overcomes the limitation of single-dimension filtering in time domain or frequency domain and does not need to refer to noise data and select base function. Only two singular values are needed to achieve a good de-noising effect, and the complexity of filtering process is reduced. When the random noise of NMR logging signal is eliminated, the waveform and minutiae of the signal can be well preserved. Inversion accuracy of T2 spectrum is improved. The combined method provides a new alternative for the noise reduction of NMR logging signal.

A blind dual color images watermarking based on singular value decomposition

In this paper, a novel image watermarking method is proposed which is based on discrete wave transformation (DWT), Hessenberg decomposition (HD), and singular value decomposition (SVD). First, in the embedding process, the host image is decomposed into a number of sub-bands through multi-level DWT, and the resulting coefficients of which are then used as the input for HD. The watermark is operated on the SVD at the same time. The watermark is finally embedded into the host image by the scaling factor. Fruit fly optimization algorithm, one of the natural-inspired optimization algorithms is devoted to find the scaling factor through the proposed objective evaluation function. The proposed method is compared to other research works under various spoof attacks, such as the filter, noise, JPEG compression, JPEG2000 compression, and sharpening attacks. The experimental results show that the proposed image watermarking method has a good trade-off between robustness and invisibility even for the watermarks with multiple sizes.