Particle swarm optimization algorithm to solve the deconvolution problem for rolling element bearing fault diagnosis

Extraction of the fault related impulses from the raw vibration signal is important for rolling element bearing fault diagnosis. Deconvolution techniques, such as minimum entropy deconvolution (MED), MED adjusted (MEDA) and maximum correlated kurtosis deconvolution (MCKD), optimal MED adjusted (OMEDA) and multipoint optimal MED adjusted (MOMEDA), are typical techniques for enhancing the impulse-like component in the fault signal. This paper introduces the particle swarm optimization (PSO) algorithm to solve the filter of deconvolution problem. The proposed approaches solve the filter coefficients of the deconvolution problems by the PSO algorithm, assisted by a generalized spherical coordinate transformation. Compared with MED, MEDA, and OMEDA, the proposed PSO-MED and PSO-OMEDA can effectively overcome the influence of large random impulses and tend to deconvolve a series of periodic impulses rather than a signal impulse. Compared with MCKD and MOMEDA, the proposed PSO-MCKD and PSO-MOMEDA can achieve good performances even when the fault period is inaccurate. The effectiveness of the proposed methods is validated by the simulated signals. The study of experimental bearing fault signal shows that the PSO based deconvolution methods delivered better performance for rolling element bearing fault detection than the traditional deconvolution methods. Additionally, the proposed methods are compared with the following two popular signal processing methods: the ensemble empirical mode decomposition (EEMD) and fast kurtogram, which are used to highlight the improved performance of the proposed methods.     

A simple model of holography and some enhanced resolution methods in electron microscopy

A simple pictorial model of electron interference effects based on an extended representation of the autocorrelation function is described and developed. Unlike Abbe's theory of transmission imaging, the model incorporates fully the effect of the loss of phase that occurs in the detector plane. The aperture transfer function and information limit (envelope function) are also incorporated with reference to the simplest scattering geometry of Young's slits. The model is then applied to holography, the diffraction phase problem, ptychography, Wigner distribution deconvolution, conventional bright-field imaging, single side-band imaging and tilt-series reconstruction. Some of these methods require an understanding of four-dimensional integral functions, but the model reduces the problem into a projection of a two-dimensional space. It is hoped that the model will help material scientists who are not specialists in imaging and diffraction theory to understand some recent developments in advanced super-resolution imaging methods.     

A computational test for the removal of plural scattering from angle-resolved energy loss spectra

A recently developed method based on matrix analysis for the removal of plural scattering from angle-resolved energy loss spectra is tested. A single loss function, Lorentzian in the energy and Gaussian in the angular variable is assumed as input for the test. Multiple scattering probabilities are simulated by summing up n-fold self-convolutions of the input function according to the Poisson distribution for incoherent n-fold scattering. The simulated profile serves as input for the retrieval algorithm, the result of which is compared with the original single-loss probability. It is concluded that the method is feasible, but not likely to be suited for routine investigations.     

Quantitative water mapping of cryosectioned cells by electron energy-loss spectroscopy

A direct technique based on electron energy-loss spectroscopy (EELS) in the scanning transmission electron microscope (STEM) has been developed to map subcellular distributions of water in frozen-hydrated biological cryosections. Previously, methods for water determination have been indirect in that they have required the cryosections to be dehydrated first. The new approach makes use of spectrum-imaging, where EELS data are collected in parallel at each pixel. Several operations are required to process the spectra including: subtraction of the detector dark current, deconvolution by the detector point-spread function, removal of plural inelastic scattering and correction for the support film. The resulting single scattering distributions are fitted to standard reference spectra at each pixel, and water content can be determined from the fitting coefficients. Although the darkfield or brightfield image from a hydrated cryosection shows minimal structure, the processed EELS image reveals strong contrast due to variations in water content. Reference spectra have been recorded from the major biomolecules (protein, lipid, carbohydrate, nucleic acid) as well as from vitrified water and crystalline ice. It has been found that quantitative results can be obtained for the majority of subcellular compartments by fitting only water and protein reference spectra, and the accuracy of the method for these compartments has been estimated as ± 3·5%. With the present instrumentation the maximum allowed dose of 2 × 10³ e/nm² limits the useful spatial resolution to around 80 nm for ± 5% precision at a single pixel. By averaging pixel intensities a value of 56·8% with a precision of ± 2·0% has been determined for the water content of liver mitochondria. The water mapping technique may prove useful for applications to cell physiology and pathophysiology.     

Design and analysis of a double superimposed chamber valveless MEMS micropump

The newly designed micropump model proposed consists of a valveless double chamber pump completely simulated and optimized for drug delivery conditions. First, the inertia force and viscous loss in relation to actuation, pressure, and frequency is considered, and then a model of the nozzle/diffuser elements is introduced. The value of the flowrate obtained from the first model is then used to determine the loss coefficients starting from geometrical properties and flow velocity. From the developed model IT analysis is performed to predict the micropump performance based on the actuation parameters and no energy loss. A single-chamber pump with geometrical dimensions equal to each of the chambers of the double-chamber pump was also developed, and the results from both models are then compared for equally applied actuation pressure and frequency. Results show that the proposed design gives a maximum flow working frequency that is about 30 per cent lower than the single chamber design, with a maximum flowrate that is 140 per cent greater than that of the single chamber. Finally, the influences of geometrical properties on flowrate, maximum flow frequency, loss coefficients, and membrane strain are examined. The results show that the nozzle/ diffuser initial width and chamber side length are the most critical dimensions of the design.     

Separation of overlapping core edges in electron energy loss spectra by multiple-least-squares fitting

A multiple-least-squares fitting procedure for quantitating electron energy loss spectra is demonstrated on some strongly overlapping core edges. The method, first applied by Shuman and Somlyo [Ultramicroscopy 21 (1987) 23], takes into account plural inelastic scattering and can be applied under conditions of non-uniform sample thickness where Fourier deconvolution techniques are invalid. By using appropriate reference spectra generated from pure compounds, quantitation of potassium and calcium (L23 edges) is possible in the presence of carbon (K edge), and sulfur in the presence of phosphorus (L23 edges). Some of the advantages and limitations of the multiple-least-squares approach are discussed.     

Axial tomographic confocal fluorescence microscopy

By physical rotation of the sample, axial tomography enables the acquisition of otherwise inaccessible spatial information from an object. In combination with confocal microscopy, the method can fundamentally improve the effective three‐dimensional (3D) resolution. In this report we present a novel method for high resolution reconstruction of confocal axial tomographic data. The method automatically determines the relative angles of rotation, aligns the data from different rotational views and reconstructs a single high resolution 3D dataset. The reconstruction makes use of a known point spread function and is based on an unconstrained maximum likelihood deconvolution performed simultaneously from multiple (in our case three) angular views. It was applied to simulated as well as to experimental confocal datasets. The gain in resolution was quantified and the effect of choice of overrelaxation factors on the speed of convergence was investigated. A clearly improved 3D resolution was obtained by axial tomography together with reconstruction as compared with reconstruction of confocal data from only a single angular view.     

Quantitative analysis of valence electron energy-loss spectra of aluminium nitride

The optical properties and electronic structure of aluminium nitride are determined using valence electron energy-loss spectroscopy in a dedicated scanning transmission electron microscope. Quantitative analysis of the experimental valence electron energy-loss spectra to determine the electronic structure encompasses single scattering deconvolution of the valence electron energy-loss spectra to calculate the energy-loss function, Kramers–Kronig analysis of the energy-loss function to reveal the complex dielectric function, transformation of the dielectric function into the optical interband transition strength via optical property relations and finally critical-point analysis of the interband transition strength. The influence of both experimental and analytical parameters on the final result was studied systematically to define and improve the understanding of the methods. To check the reliability of this technique the interband transition strength determined was compared with results of vacuum ultraviolet spectroscopy. Good agreement was found if sample preparation was taken into account. The preparation of the specimen for the transmission electron microscopy has an effect on the electronic structure. Quantitative analysis of valence electron energy-loss spectroscopy, using the methods presented, is an important and capable method to determine the electronic structure of materials and it has the benefit of high spatial resolution.     

Image-spectroscopy--II. The removal of plural scattering from extended energy-filtered series by Fourier deconvolution.

The increased spectral information obtained by acquiring an EFTEM image-series over several hundred eV allows plural scattering to be removed from loss images using standard deconvolution techniques developed for the quantification of EEL spectra. In this work, both Fourier-log and Fourier-ratio deconvolution techniques have been applied successfully to such image-series. Application of the Fourier-log technique over an energy-loss range of several hundred eV has been achieved by implementation of a novel method that extends the effective dynamic range of EFTEM image-series acquisition by over four orders of magnitude. Experimental results show that the removal of plural scattering from EFTEM image-series gives a significant improvement in quantification for thicker specimen regions. Further, the recovery of the single-scattering distribution using the Fourier-log technique over an extended energy-loss range is shown to result in an increase in both the ionisation-edge jump-ratio and the signal-to-noise ratio.     

Diagnosis of compound faults of rolling bearings through adaptive maximum correlated kurtosis deconvolution

This paper proposes a new diagnosis method based on Adaptive maximum correlated kurtosis deconvolution (AMCKD) for accurate identification of compound faults of rolling bearings. The AMCKD method combines the powerful capability of cuckoo search algorithm for global optimization with the advantage of Maximum correlated kurtosis deconvolution (MCKD) for impact signal extraction. In contrast to traditional methods, such as direct envelop spectrum, Discrete wavelet transform (DWT), and empirical mode decomposition, the proposed method extracts each fault signal related to the single failed part from the compound fault signals and effectively separates the coupled fault features. First, the original signal is processed using AMCKD method. Demodulation operation is then performed on the obtained single fault signal, and the envelope spectrum is calculated to identify the characteristic frequency information. Verification is performed on simulated and experimental signals. Results show that the proposed method is more suitable for detecting compound faults in rolling bearings compared with traditional methods. This research provides a basis for improving the monitoring and diagnosis precision of rolling bearings.     

Validity of the dipole approximation in TEM‐EELS studies

Nondipole effects in electron energy‐loss spectroscopy are evaluated in terms of deviation of the inelastic scattering from a Lorentzian angular distribution, which is assumed in established procedures for plural‐scattering deconvolution, thickness measurement, and Kramers‐Kronig analysis. The deviation appears to be small and may be outweighed by the effect of plural (elastic + inelastic) scattering, which is not removed by conventional deconvolution methods. In the core‐loss region of the spectrum, non‐Lorentzian behaviour stems from a reduction of the generalized oscillator strength from its optical value and (for energies far above an ionization threshold) formation of a Bethe‐ridge angular distribution. At incident energies above 200 keV, retardation effects further distort the angular dependence, even for core losses just above threshold. With an on‐axis collection aperture, non‐dipole effects are masked by the rapid falloff of intensity with scattering angle, but they may become important for off‐axis measurements. Near‐edge fine structure is sensitive to nondipole effects but these can be minimized by use of an angle‐limiting collection aperture. Microsc. Res. Tech. 77:773–778, 2014. © 2014 Wiley Periodicals, Inc.     

Crystal structure retrieval by maximum entropy analysis of atomic resolution incoherent images

In this paper, we discuss the application of the maximum entropy method to atomic resolution Z -contrast images acquired in a scanning transmission electron microscope. Z -contrast is an incoherent imaging technique, and can be described as a convolution between an object function (the real-space map of the columnar scattering cross-section to high angles) and a point spread function (the effective electron probe). As such, we show that the technique is ideally suited to maximum entropy analysis which can, given an electron probe distribution, retrieve the 'most likely' Z -contrast object function. Using both simulated and experimentally acquired data, we explore the capabilities of maximum entropy analysis when applied to atomic resolution Z -contrast images, drawing conclusions on both the range of applicability of the technique and the nature of the retrieved crystal structures. Ultimately, we show the way in which the combination of Z -contrast imaging with maximum entropy analysis can be used to yield important information on unexpected atomic structures.     

Image deconvolution for protein crystals

The image deconvolution technique developed for non-biological samples, which is based on the weak-phase-object approximation and principle of maximum entropy, was applied to simulated images of the biotin-binding protein streptavidin. A slight modification of the technique was introduced to solve the problem caused by the special image formation condition for biological samples. It has been shown that the modified technique is effective.     

Sparsity enhancement for blind deconvolution of ultrasonic signals in nondestructive testing application

The received signal in ultrasonic pulse-echo inspection can be modeled as a convolution between an impulse response and the reflection sequence, which is the impulse characteristic of the inspected object. Deconvolution aims at approximately inverting this process to improve the time resolution so that the overlap between echoes from closely spaced reflectors becomes small. This paper presents a modified minimum entropy blind deconvolution algorithm for deconvolving ultrasonic signals. Enhancement of the resolution is achieved by using the presented method. In addition, the presented approach will, in many cases, lead to a faster computation. A nonlinear function is the key point to the efficiency of the modified blind deconvolution algorithm, which is used to increase the sparsity of the iteration output and to decrease the influence of the added noise by replacing each iteration output by output of the nonlinear function. Simulations showed the efficiency of the modification as compared with minimum entropy deconvolution when deconvolving synthetic ultrasonic signals. Experimental results using real ultrasonic data evaluated further that the exact solution consistently yields good performance. The thickness of a thin steel sample can be calculated by the modified blind deconvolution filter with a reasonable accuracy.     

Model-based quantification of EELS spectra: Including the fine structure

An extension to model-based electron energy loss spectroscopy (EELS) quantification is reported to improve the possibility of modelling fine structure changes in electron energy loss spectra. An equalisation function is used in the energy loss near edge structure (ELNES) region to model the differences between a single atom differential cross section and the cross section for an atom in a crystal. The equalisation function can be shown to approximate the relative density of unoccupied states for the given excitation edge. On a set of 200 experimental h-BN spectra, this technique leads to statistically acceptable models resulting into unbiased estimates of relative concentrations and making the estimated precisions come very close to the Cramér-Rao lower bound (CRLB). The method greatly expands the useability of model-based EELS quantification to spectra with pronounced fine structure. Another benefit of this model is that one also gets an estimate of the unoccupied density of states for a given excitation edge, without having to do background removal and deconvolution, making the outcome intrinsically more reliable and less noisy.     

Spectroscopic identification of individual fluorophores using photoluminescence excitation spectra

The identity of a fluorophore can be ambiguous if other fluorophores or nonspecific fluorescent impurities have overlapping emission spectra. The presence of overlapping spectra makes it difficult to differentiate fluorescent species using discrete detection channels and unmixing of spectra. The unique absorption and emission signatures of fluorophores provide an opportunity for spectroscopic identification. However, absorption spectroscopy may be affected by scattering, whereas fluorescence emission spectroscopy suffers from signal loss by gratings or other dispersive optics. Photoluminescence excitation spectra, where excitation is varied and emission is detected at a fixed wavelength, allows hyperspectral imaging with a single emission filter for high signal‐to‐background ratio without any moving optics on the emission side. We report a high throughput method for measuring the photoluminescence excitation spectra of individual fluorophores using a tunable supercontinuum laser and prism‐type total internal reflection fluorescence microscope. We used the system to measure and sort the photoluminescence excitation spectra of individual Alexa dyes, fluorescent nanodiamonds (FNDs), and fluorescent polystyrene beads. We used a Gaussian mixture model with maximum likelihood estimation to objectively separate the spectra. Finally, we spectroscopically identified different species of fluorescent nanodiamonds with overlapping spectra and characterized the heterogeneity of fluorescent nanodiamonds of varying size.     

Richardson-Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution

Confocal laser scanning microscopy is a powerful and popular technique for 3D imaging of biological specimens. Although confocal microscopy images are much sharper than standard epifluorescence ones, they are still degraded by residual out-of-focus light and by Poisson noise due to photon-limited detection. Several deconvolution methods have been proposed to reduce these degradations, including the Richardson-Lucy iterative algorithm, which computes maximum likelihood estimation adapted to Poisson statistics. As this algorithm tends to amplify noise, regularization constraints based on some prior knowledge on the data have to be applied to stabilize the solution. Here, we propose to combine the Richardson-Lucy algorithm with a regularization constraint based on Total Variation, which suppresses unstable oscillations while preserving object edges. We show on simulated and real images that this constraint improves the deconvolution results as compared with the unregularized Richardson-Lucy algorithm, both visually and quantitatively.     

Enhancement of resolution in core-loss and low-loss spectroscopy in a monochromated microscope

The significant enhancement of the energy resolution in the new generation of commercially available monochromated transmission electron microscopes presents new challenges in term of selecting the correct experimental conditions and understanding the various effects that can potentially influence the quality of the EELS data. In this respect we investigated the effect of point spread function of the detector and spectrum-diffraction mixing on the energy resolution and the intensity of the zero loss peak tails. Alternative approaches to improve the energy resolution by mathematical methods have been tested. By using a simple and commonly available test case (Si L(2,3) edges) we assessed the efficiency of the deconvolution algorithms to improve the resolution. The results show that the deconvolution is not always successful in improving the resolution of the core loss EELS data and the results may not always be reliable. Contrary to this, the application of the Richardson-Lucy deconvolution algorithm on some bandgap measurements data appears to be very effective. The procedure proved successful in removing the contribution of the zero-loss peak tails and allows an easier access to spectroscopic information starting at energy losses as low as of 0.5 eV with monochromated spectra and 1 eV with the non-monochromated spectra.     

Electronic structure analysis of (In, Ga, Al) N heterostructures on the nanometre scale using EELS

In this work the local electronic structure of MOVPE-grown (In, Ga, Al) N heterostructures has been investigated by electron energy loss spectroscopy (EELS). The cold field-emission scanning transmission electron microscope (VG HB501) used was equipped with a dedicated parallel EELS system which provides high dispersions at an energy resolution of 0.35 eV with the use of subnanometre electron probes the spatial resolution of the measurements depends on the physical localization of the scattering process itself and thus is in the order of nanometres.
The low-loss region of the energy spectra gives information on plasmon excitations and transitions across the bandgap. The main problem on looking at the bandgap region of EELS spectra is to separate the bandgap signal from the fading tail of the zero-loss peak. High energy resolution and application of suitable deconvolution routines for removal of the zero-loss peak extract improved information from this energy region.
Thus the EEL spectra of different group III nitrides reveal the onset of the bandgap itself and the characteristic shape of the joint density of states. From these results the local optical properties can be deduced via a Kramers–Kronig transformation.
The data obtained show detailed structure on the energy scale and are in excellent agreement with optical ellipsometric results. In comparison with these techniques EELS methods yield a superior spatial resolution of better than 10 nm which enables detailed investigation of the effect of local defects and boundaries on the optical properties.     

直升机旋翼不平衡复合故障对机体振动的影响

在直升机旋翼不平衡单一故障试验研究的基础上,设计了桨叶后缘调整片不平衡、桨距不平衡和桨叶配重不平衡3种故障同时发生的复合故障试验,采用最大熵法估计了所采集的台体振动信号的功率谱,仿真测试表明,采用最大熵法进行功率谱估计,当与其等价的自回归模型阶数为100时,功率谱估计能充分反映台体振动信号的特征,利用正交设计方法进行复合故障试验设计并进行了风洞试验,选用L9(34)正交表,选取10 m/s风速下的横向振动1 Ω分量所对应的功率谱作为分析对象,分析结果表明,上述3种不平衡故障之间存在交互作用,其中桨距不平衡故障对机体振动水平的影响最为显著.