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This paper considers stationary regression models with near-collinear regressors. Limit theory is developed for regression estimates and test statistics in cases where the signal matrix is nearly singular in finite samples and is asymptotically degenerate. Examples include models that involve evaporating trends in the regressors that arise in conditions such as growth convergence. Structural equation models are also considered and limit theory is derived for the corresponding instrumental variable (IV) estimator, Wald test statistic, and overidentification test when the regressors are endogenous. It is shown that near-singular designs of the type considered here are not completely fatal to least squares inference, but do inevitably involve size distortion except in special Gaussian cases. In the endogenous case, IV estimation is inconsistent and both the block Wald test and Sargan overidentification test are conservative, biasing these tests in favor of the null.

The purpose of this paper is to propose a new fault feature extraction scheme for the rolling element bearing.

The generalized Stockwell transform (GST) and the singular value ratio spectrum (SVRS) methods are combined. A time-frequency distribution measurement criterion named the energy concentration measurement (ECM) is initially used to determine the parameter of the optimal GST method. Then, the optimal GST is applied to conduct a time-frequency transformation for a raw signal. Subsequently, the two-dimensional time-frequency matrix is obtained. Finally, the improved singular value decomposition (SVD) analysis is used to conduct a noise reduction of the time-frequency matrix. The SVRS is proposed to select the effective singular values. Furthermore, the time-domain feature of the impact signal is obtained by taking the inverse GST transform.

The simulated and experimental signals are used to verify the superiority of the proposed method over conventional methods. The obtained results show that the proposed method can effectively extract fault features of the rolling element bearing.

This paper mainly discusses the application of GST and SVRS methods to analyze the weak fault feature extraction problem. The next research direction is to explore the application of the Hilbert Huang transform (HHT) and variational modal decomposition (VMD) in the impact feature extraction of rolling bearing.

In the present study, a new SVRS method is proposed to select the number of effective singular values. This paper proposed an effective way to obtain the fault feature in monitoring of rotating machinery.

The purpose of this paper is to classify different conditions of the rolling element bearing (REB) using vibration signals acquired from a customized bearing test rig.

An effort has been made to develop health index (HI) based on singular values of the statistical features to classify different conditions of the REB. The vibration signals from the normal bearing (N), bearing with defect on ball (B), bearing with defect on inner race (IR) and bearing with defect on outer race (OR) have been acquired from a customized bearing test rig under variable load and speed conditions. These signals were subjected to “modified kurtosis hybrid thresholding rule” (MKHTR)-based denoising. The denoised signals were decomposed using discrete wavelet transform. A total of 17 statistical features have been extracted from the wavelet coefficients of the decomposed signal.

Singular values of the statistical features can be effectively used for REB classification.

REB are critical components of rotary machinery right across the industrial sectors. It is a well-known fact that critical bearing failures causes major breakdowns resulting in untold and most expensive downtimes that should be avoided at all costs. Hence, intelligently based bearing failure diagnosis and prognosis should be an integral part of the asset maintenance and management activity in any industry using rotary machines.

It is found that singular values of the statistical features exhibit a constant value and accordingly can be assigned to each type of bearing fault and can be used for fault characterization in practical applications. The effectiveness of this index has been established by applying this to data from Case Western Reserve University data base which is a standard bench mark data for this application. HIs minimizes the computation time when compared to fault diagnosis using soft computing techniques.

For most practical control system problems, the state variables of a system are not often available or measureable due to technical or economical constraints. In these cases, an observer-based controller design problem, which is involved with using the available information on inputs and outputs to reconstruct the unmeasured states, is desirable, and it has been wide investigated in many practical applications. However, the investigation on a discrete-time singular Markovian jumping system is few so far. This paper aims to consider an observer-based control problem for a discrete-time singular Markovian jumping system and provides a set of easy-used conditions to the proposed control law.

According to the connotation of the separation principle extended from linear systems, a mode-dependent observer and a state-feedback controller is designed and carried out independently via two sets of derived necessary and sufficient conditions in terms of linear matrix inequalities (LMIs).

A set of necessary and sufficient conditions for an admissibility analysis problem related to a discrete-time singular Markovian jumping system is derived to be a doctrinal foundation for the proposed design problems. A mode-dependent observer and a controller for such systems could be designed via two sets of strictly LMI-based synthesis conditions.

The proposed method can be applied to discrete-time singular Markovian jumping systems with transition probability p_ij > 0 rather than the ones with p_ii = 0.

The formulated problem and proposed methods have extensive applications in various fields such as power systems, electrical circuits, robot systems, chemical systems, networked control systems and interconnected large-scale systems. Take robotic networked control systems for example. It is recognized that the variance phenomena derived from network transmission, such as packets dropout, loss and disorder, are suitable for modeling as a system with Markovian jumping modes, while the dynamics of the robot systems can be described by singular systems. In addition, the packets dropout or loss might result in unreliable transmission signals which motivates an observer-based control problem.

Both of the resultant conditions of analysis and synthesis problems for a discrete-time singular Markovian jumping system are necessary and sufficient, and are formed in strict LMIs, which can be used and implemented easily via MATLAB toolbox.

The performance of the measurement matrix directly affects the quality of reconstruction of compressive sensing signal, and it is also the key to solve practical problems. In order to solve data collection problem of wireless sensor network (WSN), the authors design a kind of optimization of sparse matrix. The paper aims to discuss these issues.

Based on the sparse random matrix, it optimizes the seed vector, which regards elements in the diagonal matrix of Hadamard matrix after passing singular value decomposition (SVD). Compared with the Toeplitz matrix, it requires less number of independent random variables and the matrix information is more concentrated.

The performance of reconstruction is better than that of Gaussian random matrix. The authors also apply this matrix to the data collection scheme in WSN. The result shows that it costs less energy and reduces the collection frequency of nodes compared with general method.

The authors design a kind of optimization of sparse matrix. Based on the sparse random matrix, it optimizes the seed vector, which regards elements in the diagonal matrix of Hadamard matrix after passing SVD. Compared with the Toeplitz matrix, it requires less number of independent random variables and the matrix information is more concentrated.

This paper aims to solve the problem that strong noise interference seriously affects the direction of arrival (DOA) estimation in complex underwater acoustic environment. In this paper, a combined noise reduction algorithm and micro-electro-mechanical system (MEMS) vector hydrophone DOA estimation algorithm based on singular value decomposition (SVD), variational mode decomposition (VMD) and wavelet threshold denoising (WTD) is proposed.

Firstly, the parameters of VMD are determined by SVD, and the VMD method can decompose the signal into multiple intrinsic mode functions (IMFs). Secondly, the effective IMF component is determined according to the correlation coefficient criterion and the IMF less than the threshold is processed by WTD. Then, reconstruction is carried out to achieve the purpose of denoising and calibration baseline drift. Finally, DOA estimation is achieved by the combined directional algorithm of preprocessed signal.

Simulation and field experiments results show that the algorithm has good noise reduction and baseline drift correction effects for nonstationary underwater signals, and high-precision azimuth estimation is realized.

This research provides the basis for MEMS hydrophone detection and positioning and has great engineering significance in underwater detection system.

The purpose of this paper is to propose a fault diagnosis method for rolling bearings, in which the fault feature extraction is realized in a two-dimensional domain using scale invariant feature transform (SIFT) algorithm. This method is different from those methods extracting fault feature directly from the traditional one-dimensional domain.

The vibration signal of rolling bearings is first transformed into a two-dimensional image. Then, the SIFT algorithm is applied to the image to extract the scale invariant feature vector which is highly distinctive and insensitive to noises and working condition variation. As the extracted feature vector is high-dimensional, kernel principal component analysis (KPCA) algorithm is utilized to reduce the dimension of the feature vector, and singular value decomposition technique is used to extract the singular values of the reduced feature vector. Finally, these singular values are introduced into a support vector machine (SVM) classifier to realize fault classification.

The experiment results show a high fault classification accuracy based on the proposed method.

The proposed approach for rolling bearing fault diagnosis based on SIFT-KPCA and SVM is highly effective in the experiment. The practical value in engineering application of this method can be researched in the future.

The purpose of this paper is to highlight that the need for improved system identification methods within the domain of modal analysis increases under the impulse of the broadening field of applications, e.g., damage detection and vibro-acoustics, and the increased complexity of today’s structures. Although significant research efforts during the last two decades have resulted in an extensive number of parametric identification algorithms, most of them are certainly not directly applicable for modal parameter extraction. So, based on this, the aim of the present work is to develop a technique for modal parameter extraction from the measured signal.

A survey and classification of the different modal analysis methods are made; however, the focus of this thesis is placed on modal parameter extraction from measured time signal. Some of the methods are examined in detail, including both single-degree-of-freedom and multi-degree-of-freedom approaches using single and global frequency-response analysis concepts. The theory behind each of these various analysis methods is presented in depth, together with the development of computer programs, theoretical and experimental examples and discussion, in order to evaluate the capabilities of those methods. The problem of identifying properties of structures that possess close modes is treated in particular detail, as this is a difficult situation to handle and yet a very common one in many structures. It is essential to obtain a good model for the behavior of the structure in order to pursue various applications of experimental modal analysis (EMA), namely: updating of finite element models, structural modification, subsystem-coupling and calculation of real modes from complex modes, to name a few. This last topic is particularly important for the validation of finite element models, and for this reason, a number of different methods to calculate real modes from complex modes are presented and discussed in this paper.

In this paper, Modal parameters like mode shapes and natural frequencies are extracted using an FFT analyzer and with the help of ARTeMiS, and subsequently, an algorithm has been developed based on frequency domain decomposition (FDD) technique to check the accuracy of the results as obtained from ARTeMiS. It is observed that the frequency domain-based algorithm shows good agreement with the extracted results. Hence the following conclusion may be drawn: among several frequency domain-based algorithms for modal parameter extraction, the FDD technique is more reliable and it shows a very good agreement with the experimental results.

In the case of extraction techniques using measured data in the frequency domain, it is reported that the model using derivatives of modal parameters performed better in many situations. Lack of accurate and repeatable dynamic response measurements on complex structures in a real-life situation is a challenging problem to analyze exact modal parameters.

During the last two decades, there has been a growing interest in the domain of modal analysis. Evolved from a simple technique for troubleshooting, modal analysis has become an established technique to analyze the dynamical behavior of complex mechanical structures. Important examples are found in the automotive (cars, trucks, motorcycles), railway, maritime, aerospace (aircrafts, satellites, space shuttle), civil (bridges, buildings, offshore platforms) and heavy equipment industry.

Presently structural health monitoring has become a significantly important issue in the area of structural engineering particularly in the context of safety and future usefulness of a structure. A lot of research is being carried out in this area incorporating the modern sophisticated instrumentations and efficient numerical techniques. The dynamic approach is mostly employed to detect structural damage, due to its inherent advantage of having global and location-independent responses. EMA has been attempted by many researchers in a controlled laboratory environment. However, measuring input excitation force(s) seems to be very expensive and difficult for the health assessment of an existing real-life structure. So Ambient Vibration Analysis is a good alternative to overcome those difficulties associated with the measurement of input excitation force.

Three single bay two storey frame structure has been chosen for the experiment. The frame has been divided into six small elements. An algorithm has been developed to determine the natural frequency of those frame structures of which one is undamaged and the rest two damages in single element and double element, respectively. The experimental results from ARTeMIS and from developed algorithm have been compared to verify the effectiveness of the developed algorithm. Modal parameters like mode shapes and natural frequencies are extracted using an FFT analyzer and with the help of ARTeMiS, and subsequently, an algorithm has been programmed in MATLAB based on the FDD technique to check the accuracy of the results as obtained from ARTeMiS. Using singular value decomposition, the power Spectral density function matrix is decomposed using the MATLAB program. It is observed that the frequency domain-based algorithm shows good consistency with the extracted results.

In today’s digital world, real-time health monitoring is becoming a most important challenge in the field of medical research. Body signals such as electrocardiogram (ECG), electromyogram and electroencephalogram (EEG) are produced in human body. This continuous monitoring generates huge count of data and thus an efficient method is required to shrink the size of the obtained large data. Compressed sensing (CS) is one of the techniques used to compress the data size. This technique is most used in certain applications, where the size of data is huge or the data acquisition process is too expensive to gather data from vast count of samples at Nyquist rate. This paper aims to propose Lion Mutated Crow search Algorithm (LM-CSA), to improve the performance of the LMCSA model.

A new CS algorithm is exploited in this paper, where the compression process undergoes three stages: designing of stable measurement matrix, signal compression and signal reconstruction. Here, the compression process falls under certain working principle, and is as follows: signal transformation, computation of Θ and normalization. As the main contribution, the theta value evaluation is proceeded by a new “Enhanced bi-orthogonal wavelet filter.” The enhancement is given under the scaling coefficients, where they are optimally tuned for processing the compression. However, the way of tuning seems to be the great crisis, and hence this work seeks the strategy of meta-heuristic algorithms. Moreover, a new hybrid algorithm is introduced that solves the above mentioned optimization inconsistency. The proposed algorithm is named as “Lion Mutated Crow search Algorithm (LM-CSA),” which is the hybridization of crow search algorithm (CSA) and lion algorithm (LA) to enhance the performance of the LM-CSA model.

Finally, the proposed LM-CSA model is compared over the traditional models in terms of certain error measures such as mean error percentage (MEP), symmetric mean absolute percentage error (SMAPE), mean absolute scaled error, mean absolute error (MAE), root mean square error, L1-norm and L2-normand infinity-norm. For ECG analysis, under bior 3.1, LM-CSA is 56.6, 62.5 and 81.5% better than bi-orthogonal wavelet in terms of MEP, SMAPE and MAE, respectively. Under bior 3.7 for ECG analysis, LM-CSA is 0.15% better than genetic algorithm (GA), 0.10% superior to particle search optimization (PSO), 0.22% superior to firefly (FF), 0.22% superior to CSA and 0.14% superior to LA, respectively, in terms of L1-norm. Further, for EEG analysis, LM-CSA is 86.9 and 91.2% better than the traditional bi-orthogonal wavelet under bior 3.1. Under bior 3.3, LM-CSA is 91.7 and 73.12% better than the bi-orthogonal wavelet in terms of MAE and MEP, respectively. Under bior 3.5 for EEG, L1-norm of LM-CSA is 0.64% superior to GA, 0.43% superior to PSO, 0.62% superior to FF, 0.84% superior to CSA and 0.60% better than LA, respectively.

This paper presents a novel CS framework using LM-CSA algorithm for EEG and ECG signal compression. To the best of the authors’ knowledge, this is the first work to use LM-CSA with enhanced bi-orthogonal wavelet filter for enhancing the CS capability as well reducing the errors.

This paper aims to propose a noise-robust method to estimate the frequency of the reflective echo to reduce the negative effects of noise and improve the accuracy and resolution of a resonant surface acoustic wave (SAW) sensor.

The proposed approach exploits the singular value decomposition to obtain the frequency information of a SAW response signal and overcome the noise influences.

Compared with the commonly used Fourier transform (FT) method, the accuracy and resolution improvement of the proposed method used in the SAW sensor is validated.

The system using the proposed method delivers lesser standard deviation, that is, delivers higher performance than the conventional system using the fast FT method.