Maximum Entropy Deconvolution Research Articles

Maximum negative entropy deconvolution and its application to bearing condition monitoring

Blind deconvolution (BD) has proven to be an effective approach to detecting repetitive transients caused by bearing faults. However, BD suffers from instability issues including excessive sensitivity of kurtosis-guided BD methods to the single impulse and high computational time cost of the eigenvector algorithm-aided BD methods. To address these critical issues, this paper proposed a novel BD method maximizing negative entropy (NE), shortened as maximum negative entropy deconvolution (MNED). MNED utilizes NE instead of kurtosis as the optimization metric and optimizes the filter coefficients through the objective function method. The effectiveness of MNED in enhancing repetitive transients is illustrated through a simulation case and two experimental cases. A quantitative comparison with three existing BD methods demonstrates the advantages of MNED in fault detection and computational efficiency. In addition, the performance of the four methods under different filter lengths and external shocks is compared. MNED exhibits lower sensitivity to random impulse noise than the kurtosis-guided BD methods and higher computational efficiency than the BD methods based on the eigenvalue algorithm. The simulation and experimental results demonstrate that MNED is a robust and cost-effective method for bearing fault diagnosis and condition monitoring.

Research on the detection of axle abnormal noise based on maximum autocorrelation kurtosis deconvolution

The axle off-line detection is an important link to ensure the sound quality of the axle. The traditional methods mainly rely on condition indicators, psychoacoustic parameters and artificial intelligence, in which the generation mechanism of the abnormal signal is ignored, thus leading to low accuracy and poor interpretability. To solve these problems, a vehicle axle abnormal sound detection method based on abnormal sound mechanism is proposed in this paper. Firstly, the sound quality of 30 newly produced axles is determined by subjective evaluation, and it is clear that the tooth frequency impulse is the main reason for the abnormal sound of axles. Then, a new objective function, autocorrelation kurtosis, is used to deconvolute the axle vibration signal for the periodic impulse feature. Simulation and experimental results show that the proposed maximum autocorrelation kurtosis deconvolution (MACKD) is more effective than maximum correlation kurtosis deconvolution (MCKD) and minimum entropy deconvolution (MED). On this basis, the impulse autocorrelation kurtosis index (IACK) is constructed and used to quantify the abnormal sound of the axle. The results show that the correlation between the proposed index and the subjective evaluation results is more than 0.9, which can better identify the sound quality of the axle.

Research on Fault Extraction Method of CYCBD Based on Seagull Optimization Algorithm

Maximum cyclostationarity blind deconvolution (CYCBD) can recover the periodic impulses from mixed fault signals comprised by noise and periodic impulses. In recent years, blind deconvolution has been widely used in fault diagnosis. However, it requires a preset of filter length, and inappropriate filter length may cause the inaccurate extraction of fault signal. Therefore, in order to determine filter length adaptively, a method to optimize CYCBD by using the seagull optimization algorithm (SOA) is proposed in this paper. In this method, the ratio of SNR to kurtosis is used as the objective function; firstly, SOA is used to search the optimal filter length in CYCBD by iteration, and then it uses the optimal filter length to perform CYCBD; finally, the frequency-domain waveform is determined through Fourier transformation. The method proposed is applied to the fault extraction of a simulated signal and a test vibration signal of the closed power flow gearbox test bed, and the fault frequency is successfully extracted, in addition, using maximum correlation kurtosis deconvolution (MCKD) and multipoint optimal minimum entropy deconvolution adjusted (MOMEDA) to compare with CYCBD-SOA, which validated availability of the proposed method.

Improved Approach for the Maximum Entropy Deconvolution Problem.

The probability density function (pdf) valid for the Gaussian case is often applied for describing the convolutional noise pdf in the blind adaptive deconvolution problem, although it is known that it can be applied only at the latter stages of the deconvolution process, where the convolutional noise pdf tends to be approximately Gaussian. Recently, the deconvolutional noise pdf was approximated with the Edgeworth Expansion and with the Maximum Entropy density function for the 16 Quadrature Amplitude Modulation (QAM) input but no equalization performance improvement was seen for the hard channel case with the equalization algorithm based on the Maximum Entropy density function approach for the convolutional noise pdf compared with the original Maximum Entropy algorithm, while for the Edgeworth Expansion approximation technique, additional predefined parameters were needed in the algorithm. In this paper, the Generalized Gaussian density (GGD) function and the Edgeworth Expansion are applied for approximating the convolutional noise pdf for the 16 QAM input case, with no need for additional predefined parameters in the obtained equalization method. Simulation results indicate that improved equalization performance is obtained from the convergence time point of view of approximately 15,000 symbols for the hard channel case with our new proposed equalization method based on the new model for the convolutional noise pdf compared to the original Maximum Entropy algorithm. By convergence time, we mean the number of symbols required to reach a residual inter-symbol-interference (ISI) for which reliable decisions can be made on the equalized output sequence.

Adapted dictionary-free orthogonal matching pursuit and 0-1 programming to solve the isolation and diagnosis of bearing and gear compound faults

In the fault diagnosis of bearings, the high flexibility of the asymmetric Gaussian chirplet model enables the adapted dictionary-free orthogonal matching pursuit to manifest good performance. Since this method does not rely on predetermined dictionaries, it has potential advantages as well, especially for the impulses caused by compound faults that are multiple type’s combination. Benefiting from the sparse representation architecture, the fault isolation can be skillfully converted into a 0-1 programming problem for elements selection in sparse vector, which may become one of the breakthroughs in solving compound faults’ isolation. Consequently, this paper attempts to give a solution using signal processing. Specifically, the maximum entropy deconvolution adjusted technique is used for preprocessing, which includes noise reduction and impulsiveness enhancement. Notch filter and spectral subtraction is utilized for impulses screening and extraction, and spectrum is employed for fault diagnosis. Simulation analysis and experimental tests verify the proposed method, whose results illustrated the potentiality to response the compound fault isolation and diagnosis.

A Novel Fault Diagnosis Method of Gearbox Based on Maximum Kurtosis Spectral Entropy Deconvolution

Minimum entropy deconvolution (MED) is widely used in the gearbox fault diagnosis because it can enhance the energy of the impact signal. However, it is sensitive to single abnormal impulsive oscillation. This is because it takes kurtosis as the objective function and solves the optimal filter by iteration. In addition, the filter length is not adaptive and needs to be determined artificially. This paper proposes a maximum kurtosis spectral entropy deconvolution (MKSED) method and applies it to bearing fault diagnosis. Considering that the kurtosis spectral entropy has the advantage of highlighting the continuous impact oscillation, the kurtosis spectral entropy is chosen as the objective function of deconvolution. At the same time, kurtosis spectral entropy is also used as the fitness function of improved local particle swarm optimization algorithm (LPSO), and the filter length is optimized by LPSO, which makes that MKSED adaptively determines the length of the filter while solving the deconvolution, so that it can accurately extract the continuous pulse signal. The results of the simulation signal analysis show that the proposed MKSED method is superior to MED, and the proposed method is applied to bearing fault diagnosis, which verifies its ability to extract continuous impact.

Systematic Two-Dimensional DRT-Analysis of Battery and Fuel Cell Impedance Data

Electrochemical Impedance Spectroscopy (EIS) has become an important tool for the analysis of batteries and fuel cells. Thus, the interest in the ongoing development of this technique is high. The major drawback of EIS is the ambiguity caused by the necessity to select a particular model for fitting the experimental data. One approach to mitigate this problem is the analysis of impedance data by the distribution of relaxation times (DRT) of the underlying physico-chemical processes, which might be the reason for its recent popularity [1-3]. The DRT can be calculated by a variety of methods, such as Fourier filtering [4], maximum-entropy deconvolution [5], least-squares deconvolution [6], evolutionary programming [7] or regularization [8]. The advantage of regularization is its usability without any a priori knowledge of the system. In this work, an evolution of the widely applied Tikhonov regularization in standard form [9] with an RC kernel is presented. The algorithm is using a uniform penalty. It has the advantage that narrow, high amplitude features are less broadened than low amplitude features in the same DRT spectrum and that it is less susceptible to unphysical oscillations [10]. This allows us to avoid a non-negativity constraint or similar penalties, therefore inductive and capacitive features can be unraveled in the spectrum by their opposite sign. In addition, by performing the regularization on two-dimensional (2D) data even if only one dimension is inverted, an improved resolution in the DRT dimension and smoother features in the non-inverted dimension are achieved. With peak-fitting algorithms each identified process is quantified and subsequently back-transformed into the frequency domain. By this, the contributions of the different processes to the overall impedance are visualized. Regularization is, in general, vulnerable to artifacts [11]. Hence checking the validity of the inverted data to prevent false interpretations is necessary, for which a procedure is described. 2D-DRT is used for the analysis of impedance data obtained from measurements of solid oxide fuel cells (SOFC) and lithium-ion batteries (LIB). For instance, for the SOFC the impedance measurements were performed for varying temperatures between 700°C and 900°C and potentials between 1200 mV and 700 mV. With this approach five different physico-chemical processes could be quantified in the frequency range between 100 mHz and 100 kHz which is in accordance with the literature [12].

Deconvolving Smooth Residence Time Distributions from Raw Solute Transport Data

A residence time distribution (RTD) provides a complete model of longitudinal mixing effects that can be robustly derived from experimental solute transport data. Maximum entropy deconvolution has been shown to recover RTDs from preprocessed laboratory data. However, data preprocessing is time consuming and may introduce errors. Assuming data were recorded using sensors with a linear response, it should be possible to deconvolve raw data without preprocessing. This paper uses synthetically generated raw data to demonstrate that the quality of the deconvolved RTD remains satisfactory when preprocessing steps involving data cropping or calibration are skipped. Provided noise levels are relatively low, filtering steps may also be omitted. However, a rough subtraction of background concentration is recommended as a minimal preprocessing step. Deconvolved RTDs often include small-scale fluctuations that are inconsistent with a well-mixed fully turbulent system. These are believed to be associated with oversampling and/or unsuitable interpolation functions used in the maximum entropy deconvolution process. This paper describes a new interpolation function—linear interpolation with an automatic moving average (LAMA)—and demonstrates that, in combination with fewer sample points (e.g., 20), it enables smoother RTDs to be generated. The two improvements, to deconvolve raw data and to generate smoother RTDs, have been validated with experimental data. Raw solute transport traces collected from a river were deconvolved after background subtraction. The deconvolved RTDs compare favorably with those generated from the more traditional advection-dispersion equation (ADE) and aggregated dead zone (ADZ) models, but provide more detail of mixing processes. A laboratory manhole solute transport data set was deconvolved with and without preprocessing using 40 sample points and linear interpolation. The raw data were also deconvolved using 20 sample points and LAMA interpolation. The two sets of RTDs deconvolved from the raw data show the same mixing trends as those deconvolved from preprocessed data. However, those deconvolved with LAMA interpolation and 20 sample points are significantly smoother.

Configuring Maximum Entropy Deconvolution for the Identification of Residence Time Distributions in Solute Transport Applications

The advection-dispersion equation (ADE) or aggregated dead zone (ADZ) models and their derivatives are frequently used to describe mixing processes within rivers, channels, pipes, and urban drainage structures. The residence time distribution (RTD) provides a nonparametric model that may describe mixing effects in complex mixing contexts more completely. Identifying an RTD from laboratory data requires deconvolution. Previous studies have successfully applied maximum entropy deconvolution to solute transport data, with RTD subsampling used for computational simplification. However, this requires a number of configuration settings which have to date not been rigorously investigated. Four settings are investigated here: the number and distribution of sample points, the constraint function, and the maximum number of iterations. Configuration options for each setting have been systematically assessed with reference to representative solute transport data by comparing the goodness-of-fit of recorded and predicted downstream profiles using the Nash-Sutcliffe efficiency index, evaluating RTD smoothness with a measure of entropy, and through consideration of the mass-balance of the RTD. New methods for defining sample point distribution are proposed. The results indicate that goodness-of-fit is most sensitive to constraint function and that smoothness is most sensitive to the number and distribution of sample points. A set of configuration options that includes a new sample point distribution is shown to perform robustly for a representative range of laboratory solute transport data.

Spectrum unfolding in X-ray spectrometry using the maximum entropy method

The solution of the unfolding problem is an ever-present issue in X-ray spectrometry. The maximum entropy technique solves this problem by taking advantage of some known a priori physical information and by ensuring an outcome with only positive values. This method is implemented in MAXED (MAXimum Entropy Deconvolution), a software code contained in the package UMG (Unfolding with MAXED and GRAVEL) developed at PTB and distributed by NEA Data Bank. This package contains also the code GRAVEL (used to estimate the precision of the solution). This article introduces the new code UMESTRAT (Unfolding Maximum Entropy STRATegy) which applies a semi-automatic strategy to solve the unfolding problem by using a suitable combination of MAXED and GRAVEL for applications in X-ray spectrometry. Some examples of the use of UMESTRAT are shown, demonstrating its capability to remove detector artifacts from the measured spectrum consistently with the model used for the detector response function (DRF).

The precise timeline of transcriptional regulation reveals causation in mouse somitogenesis network

BackgroundIn vertebrate development, the segmental pattern of the body axis is established as somites, masses of mesoderm distributed along the two sides of the neural tube, are formed sequentially in the anterior-posterior axis. This mechanism depends on waves of gene expression associated with the Notch, Fgf and Wnt pathways. The underlying transcriptional regulation has been studied by whole-transcriptome mRNA profiling; however, interpretation of the results is limited by poor resolution, noisy data, small sample size and by the absence of a wall clock to assign exact time for recorded points.ResultsWe present a method of Maximum Entropy deconvolution in both space and time and apply it to extract, from microarray timecourse data, the full spatiotemporal expression profiles of genes involved in mouse somitogenesis. For regulated genes, we have reconstructed the temporal profiles and determined the timing of expression peaks along the somite cycle to a single-minute resolution. Our results also indicate the presence of a new class of genes (including Raf1 and Hes7) with two peaks of activity in two distinct phases of the somite cycle. We demonstrate that the timeline of gene expression precisely reflects their functions in the biochemical pathways and the direction of causation in the regulatory networks.ConclusionsBy applying a novel framework for data analysis, we have shown a striking correspondence between gene expression times and their interactions and regulations during somitogenesis. These results prove the key role of finely tuned transcriptional regulation in the process. The presented method can be readily applied to studying somite formation in other datasets and species, and to other spatiotemporal processes.

Fast, automated implementation of temporally precise blind deconvolution of multiphasic excitatory postsynaptic currents.

Records of excitatory postsynaptic currents (EPSCs) are often complex, with overlapping signals that display a large range of amplitudes. Statistical analysis of the kinetics and amplitudes of such complex EPSCs is nonetheless essential to the understanding of transmitter release. We therefore developed a maximum-likelihood blind deconvolution algorithm to detect exocytotic events in complex EPSC records. The algorithm is capable of characterizing the kinetics of the prototypical EPSC as well as delineating individual release events at higher temporal resolution than other extant methods. The approach also accommodates data with low signal-to-noise ratios and those with substantial overlaps between events. We demonstrated the algorithm’s efficacy on paired whole-cell electrode recordings and synthetic data of high complexity. Using the algorithm to align EPSCs, we characterized their kinetics in a parameter-free way. Combining this approach with maximum-entropy deconvolution, we were able to identify independent release events in complex records at a temporal resolution of less than 250 µs. We determined that the increase in total postsynaptic current associated with depolarization of the presynaptic cell stems primarily from an increase in the rate of EPSCs rather than an increase in their amplitude. Finally, we found that fluctuations owing to postsynaptic receptor kinetics and experimental noise, as well as the model dependence of the deconvolution process, explain our inability to observe quantized peaks in histograms of EPSC amplitudes from physiological recordings.

Reconstruction of three-dimensional chemiluminescence images with a maximum entropy deconvolution algorithm

Three-dimensional (3D) images of flame emission are reported using a single direction of optical access. A Cassegrain system was designed with narrow depth of field. Images from this system are dominated by emission from the focused object plane with defocused contributions from out-of-plane structures. Translation of one mirror in the system allows for scanning the object plane through the flame. Images were taken at various depths to create a family of images. Reconstruction of the 3D flame structure was accomplished using a maximum entropy algorithm adapted for use with 3D imaging. Spatial resolution in the direction of imaging is examined using laminar flames with variable offset.

Unfolding of Neutron Energy Spectra With Fisher Regularisation

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> A Monte Carlo unfolding method has been developed for neutron spectrometry with foil activation measurements. It is based on minimising least squares differences between measured and calculated activities under a Fisher regularisation constraint. The performance of the unfolding procedure is first illustrated by a set of 20 foil detectors to simulate reaction rates calculated for a typical neutron reactor energy spectrum. A demonstration of the method is next made using measured reaction rates of the Arkansas Nuclear One power plant benchmark spectrum of the Neutron Metrology File (NMF-90). Results of the method are compared with those obtained by the MAXimum Entropy Deconvolution (MAXED) code using the same input data and are found to be in good agreement with the measured activities. Our procedure has an advantage in unfolding the neutron energy distribution when an a priori solution for an underdetermined unfolding problem is lacking. This is illustrated by unfolding the fast neutron beam spectrum of the <emphasis emphasistype="smcaps">MedApp</emphasis> facility at the nuclear reactor FRM-II in the SAND-II expanded 640-energy group structure, using a set of 22 experimental activation rates without a guess solution. </para>

Measurements of Cosmic-Ray Neutron Energy Spectra from Thermal to 15 MeV with Bonner Ball Neutron Detector in Aircraft

Cosmic-ray neutron energy spectra from thermal to 15MeV were measured with a multimoderator spectrometer known as the Bonner Ball Neutron Detector (BBND) at aviation altitude (9–11 km). Four flights were carried out around Nagoya Airport in Japan. The measured data were unfolded using the maximum entropy deconvolution code MAXED, and the derived spectra agreed with the calculated results using the PHITS-based analytical radiation model in the atmosphere (PARMA). The results of the in-flight measurement verified the accuracy of model calculation in regard to the neutrons within a certain energy range.

Measurements of Cosmic-Ray Neutron Energy Spectra from Thermal to 15 MeV with Bonner Ball Neutron Detector in Aircraft

Cosmic-ray neutron energy spectra from thermal to 15MeV were measured with a multimoderator spectrometer known as the Bonner Ball Neutron Detector (BBND) at aviation altitude (9–11 km). Four flights were carried out around Nagoya Airport in Japan. The measured data were unfolded using the maximum entropy deconvolution code MAXED, and the derived spectra agreed with the calculated results using the PHITS-based analytical radiation model in the atmosphere (PARMA). The results of the in-flight measurement verified the accuracy of model calculation in regard to the neutrons within a certain energy range.

Local crystal structure analysis with several picometer precision using scanning transmission electron microscopy

We report a local crystal structure analysis with a high precision of several picometers on the basis of scanning transmission electron microscopy (STEM). Advanced annular dark-field (ADF) imaging has been demonstrated using software-based experimental and data-processing techniques, such as the improvement of signal-to-noise ratio, the reduction of image distortion, the quantification of experimental parameters (e.g. , thickness and defocus) and the resolution enhancement by maximum-entropy deconvolution. The accuracy in the atom position measurement depends on the validity of the incoherent imaging approximation, in which an ADF image is described as the convolution between the incident probe profile and scattering objects. Although the qualitative interpretation of ADF image contrast is possible for a wide range of specimen thicknesses, the direct observation of a crystal structure with deep-sub-angstrom accuracy requires a thin specimen (e.g., 10 nm), as well as observation of the structure image by conventional high-resolution transmission electron microscopy.

Reconstruction of the history of anthropogenic CO2 concentrations in the ocean

The release of fossil fuel CO(2) to the atmosphere by human activity has been implicated as the predominant cause of recent global climate change. The ocean plays a crucial role in mitigating the effects of this perturbation to the climate system, sequestering 20 to 35 per cent of anthropogenic CO(2) emissions. Although much progress has been made in recent years in understanding and quantifying this sink, considerable uncertainties remain as to the distribution of anthropogenic CO(2) in the ocean, its rate of uptake over the industrial era, and the relative roles of the ocean and terrestrial biosphere in anthropogenic CO(2) sequestration. Here we address these questions by presenting an observationally based reconstruction of the spatially resolved, time-dependent history of anthropogenic carbon in the ocean over the industrial era. Our approach is based on the recognition that the transport of tracers in the ocean can be described by a Green's function, which we estimate from tracer data using a maximum entropy deconvolution technique. Our results indicate that ocean uptake of anthropogenic CO(2) has increased sharply since the 1950s, with a small decline in the rate of increase in the last few decades. We estimate the inventory and uptake rate of anthropogenic CO(2) in 2008 at 140 +/- 25 Pg C and 2.3 +/- 0.6 Pg C yr(-1), respectively. We find that the Southern Ocean is the primary conduit by which this CO(2) enters the ocean (contributing over 40 per cent of the anthropogenic CO(2) inventory in the ocean in 2008). Our results also suggest that the terrestrial biosphere was a source of CO(2) until the 1940s, subsequently turning into a sink. Taken over the entire industrial period, and accounting for uncertainties, we estimate that the terrestrial biosphere has been anywhere from neutral to a net source of CO(2), contributing up to half as much CO(2) as has been taken up by the ocean over the same period.

Size-exclusion chromatography as a linear transfer system: Purification of human influenza virus as an example

Preparative size-exclusion chromatography suffers from low selectivity and productivity. Empirical optimization of operating conditions constitutes a laborious task due to many parameters. Here, a modeling framework based on linear systems theory is presented for predicting the influence of volume overloading. Impulse-responses characterizing system behavior are derived from experimental data by maximum entropy deconvolution. Theoretical derivations are validated experimentally by study of a model system and chromatography of human influenza virus. By application of the theory it is demonstrated how group separation operations can be optimized with respect to yield, purity, productivity and dilution of the product.

Nonparametric Prediction of Free-light Chain Generation in Multiple Myeloma Patients

Multiple Myeloma is a plasma cell cancer that produces excess Free Light Chains (FLC). Patients with this condition are treated with dialysis and chemotherapy. A previous compartmental model developed by Evans et al. [2006] described the removal of FLC through a hemodialysis membrane. In this model all rate constants were considered linear and the production of FLC a constant input function. It is known that the system rate constants and inputs are non-linear in nature due to the membrane dynamics and the use of chemotherapy to retard the production FLC producing cells. This study describes the use of maximum entropy deconvolution, in conjunction with a non-linear compartmental model, to recreate the FLC production rate in a non-parametric form, without the need for assumptions that are not supported by available data. Input functions are reconstructed from four different patients with a range of dialysis durations and FLC plasma concentrations to investigate the possible effects of chemotherapy on the underlying FLC production.