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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.

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 dynamics of coupling between spectrum and resolvent under ε‐perturbations of operator and matrix spectra are studied both theoretically and numerically. The phenomenon of non‐trivial pseudospectra encountered in these dynamics is treated by relating information in the complex plane to the behaviour of operators and matrices. On a number of numerical results we show how an intrinsic blend of theory with symbolic and numerical computations can be used effectively for the analysis of spectral problems arising from engineering applications.

The chapter considers parameter identification, estimation, and model diagnostics in medium scale DSGE models from a frequency domain perspective using the framework developed in Qu and Tkachenko (2012). The analysis uses Smets and Wouters (2007) as an illustrative example, motivated by the fact that it has become a workhorse model in the DSGE literature. For identification, in addition to checking parameter identifiability, we derive the non-identification curve to depict parameter values that yield observational equivalence, revealing which and how many parameters need to be fixed to achieve local identification. For estimation and inference, we contrast estimates obtained using the full spectrum with those using only the business cycle frequencies to find notably different parameter values and impulse response functions. A further comparison between the nonparametrically estimated and model implied spectra suggests that the business cycle based method delivers better estimates of the features that the model is intended to capture. Overall, the results suggest that the frequency domain based approach, in part due to its ability to handle subsets of frequencies, constitutes a flexible framework for studying medium scale DSGE models.

The aim of this paper is to propose a new coning correction algorithm, based on the singular perturbation technique, for the attitude update computation with non‐ideal angular rate information.

Unlike conventional coning correction algorithms, the new method uses angular rate two‐time scale model to construct the coning correction term of attitude update. In order to achieve balanced real/pseudo coning correction performance, the selection guidelines of the new algorithm parameters are established.

Performance of the new algorithm is evaluated by comparison with the conventional algorithm in no ideal sensors undergoing stochastic coning environments. The accuracy of attitude update can be improved effectively with reduced computational workload by using this new coning algorithm as compared with conventional ones.

The proposed coning correction algorithm can be implemented with angular rate sensors in UAV (unmanned aerial vehicle) and other aircrafts attitude estimation for navigation and control applications.

Singular perturbation is an effective method for structuring coning correction algorithm with filtered angular rate outputs in stochastic coning environments. The improved coning correction algorithm based on singular perturbations reduces the real and pseudo coning effects effectively as compared with conventional ones. It is proved to be valid for improvement of accuracy with reduced computations of the attitude update.

This paper presents a spectral multidomain method for solving the Navier‐Stokes equations in the vorticity‐stream function formulation. The algorithm is based on an extensive use of the influence matrix technique and so leads to a direct method without any iterative process. Numerical results concerning the Czochralski melt configuration are reported and compared with spectral monodomain solutions to show the advantage of the domain decomposition for such a problem which solution presents a singular behaviour.

Early fault detection of bearing plays an increasingly important role in the operation of rotating machinery. Based on the properties of early fault signal of bearing, this paper aims to describe a novel hybrid early fault detection method of bearings.

In adaptive variational mode decomposition (AVMD), an adaptive strategy is proposed to select the optimal decomposition level K of variational mode decomposition. Then, a criterion based on envelope entropy is applied to select the optimal intrinsic mode functions (OIMF), which contains most useful fault information. Afterwards, local tangent space alignment (LTSA) is used to denoising of OIMF. The envelope spectrum of the OIMF is used to analyze the fault frequency, thereby detecting the fault. Experiments are conducted in a simulated signal and two experimental vibration signals of bearings to verify the effect of the new method.

The results show that the proposed method yields a good capability of detecting bearing fault at an early stage. The new method can extract more useful information and can reduce noise, which can provide better detection accuracy compared with the other two methods.

An adaptive strategy based on center frequency is proposed to select the optimal decomposition level of variational mode decomposition. Envelope entropy is used to fault feature selection. Combining the advantage of the AVMD-envelope entropy and LTSA, which suits the nature of the early fault signal. So, the proposed method has better detection accuracy, which provides a good alternative for early fault detection of bearings.

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.

Crack damage detection for aluminum alloy materials using fiber Bragg Grating (FBG) sensor is a kind of structure health monitoring. In this paper, the damage index of full width at half maximum (FWHM) was extracted from the distorted reflection spectra caused by the crack-tip inhomogeneous strain field, so as to explain the crack propagation behaviors.

The FWHM variations were also investigated through combining the theoretical calculations with simulation and experimental analyses. The transfer matrix algorithm was developed to explore the mechanism by which FWHM changed with the linear and quadratic strain. Moreover, the crack-tip inhomogeneous strain field on the specimen surface was computed according to the digital image correlation measurement during the experiments.

The experimental results demonstrated that the saltation points in FWHM curve accorded with the moments of crack propagation to FBG sensors.

The interpretation of reflected spectrum deformation mechanism with crack propagation was analyzed based on both simulations and experiments, and then the performance of potential damage features – FWHM were proposed and evaluated. According to the correlation between the damage characteristic and the crack-tip location, the crack-tip of the specimen could be measured rapidly and accurately with this technique.

An approach is presented for the development of a predictive maintenance system for rotor‐dynamic pumps, which focuses on the diagnosis of abnormal events related to fluid‐dynamic operating conditions. This methodology is based on an experimental characterization of the dynamic response of the pump under different loads and operation anomalies. The procedure has been put into practice on a medium‐sized centrifugal pump. The results obtained show that a simple spectral analysis of the pressure signals captured at either the inlet or the outlet of the pump can provide sufficient decision criteria to constitute the basis for a diagnostic system. This was not true however when analyzing signals of acceleration at the pump casing.