Order Statistic Filters Research Articles

An improved parameterless empirical wavelet transform for incipient fault identification of wheelset bearing.

The empirical wavelet transform (EWT), along with its adaptable spectrum segmentation technique, finds extensive application in the incipient detection of rolling bearing faults. However, determining mode boundaries adaptively under strong noise interference remains a substantial challenge. Herein, an improved parameterless EWT based on the order statistics filter (OSF) is proposed to overcome this shortcoming. This approach replaces the Fourier spectrum with its envelope spectrum through OSF, and the local minima of the envelope spectrum are selected as the initial boundary to obtain the initial empirical modes. Furthermore, the adjacent initial empirical modes are combined using Pearson's correlation coefficient, and the final number and boundaries of empirical modes are automatically determined using the mean envelope entropy. The advantages of the proposed method are demonstrated through an accelerated degradation bearing test bench and a wheelset-bearing test bench, as well as by comparing it with empirical mode decomposition (EMD), ensemble empirical mode decomposition (EEMD), and Autogram.

A Fast and Adaptive Empirical Mode Decomposition Method and Its Application in Rolling Bearing Fault Diagnosis

Although the ensemble empirical mode decomposition (EEMD) method and the complementary EEMD (CEEMD) method can greatly improve the mode mixing of the original empirical mode decomposition (EMD) method, the difference in white noise amplitude and the number of ensemble trials have a great influence on the decomposition results, and the low computational efficiency cannot meet the requirements of the online monitoring system. To solve these problems, a fast and adaptive EMD (FAEMD) method was proposed in this article, which combines the advantages of the order statistics filter (OSF) with the original EMD. First, the upper envelope and lower envelope of the original signal were drawn by using the OSF. Then, the original signal was decomposed into a series of intrinsic mode functions (IMFs) by the mean envelopes. Finally, the fault feature information was obtained by using the envelope spectrum analysis. The simulation signal and two groups of test fault signals were taken as examples to verify the effectiveness of the proposed method. Compared with EMD, CEEMD, and CEEMDAN methods, FAEMD can effectively extract the key feature information of fault signals and has strong practicability because of the low calculation cost.

Adaptive Swarm Decomposition Algorithm for Compound Fault Diagnosis of Rolling Bearings

The feature extraction of compound faults is still considered the bottle neck task of machinery fault diagnosis. In this article, a novel adaptive swarm decomposition (ASWD) algorithm based on fine to coarse (FTC) segmentation is proposed for compound fault detection of rolling bearings. Firstly, the number of oscillating components that affects the results of ASWD is automatically determined by the order statistics filter and energy spectrum segmentation method without any prior knowledge. Secondly, the Teager energy kurtosis (TEK) of successively extracted components is employed as the indicator to evaluate the effectiveness of iterations. This not only setups the swarm decomposition (SWD) threshold, but also improves the performance of periodic impulses separation. Finally, ASWD is applied to intelligently separate the different oscillating components and suppress the redundant decomposition. The testing results of ASWD on the simulation and real cases indicate that ASWD can effectively extract compound fault impulses from multicomponent vibration signals. The comparison between SWD and other decomposition methods further verifies the superiority of ASWD. The characteristic frequency intensity coefficient (CFIC) of ASWD is increased by 34.2%, 49.2%, and 56.5% in the three cases, respectively, than SWD, variational mode decomposition (VMD), and ensemble empirical mode decomposition (EEMD).

Application of enhanced empirical wavelet transform and correlation kurtosis in bearing fault diagnosis

The traditional empirical wavelet transform (EWT) based on the Meyer wavelet and scale-space method can decompose a signal into several empirical modes. However, this method is not effective in dealing with strong noise and non-stationary signals, which may lead to modal mixing or even decompose too many invalid components. For this purpose, a method based on the combination of enhanced empirical wavelet transform (EEWT) and correlation kurtosis (CK) is proposed in this paper. Firstly, the EEWT is used to segment the spectrum based on the characteristics of the spectrum fluctuations. It uses the minimum points of the envelope as the boundaries of the segmented spectrum. Secondly, a filter bank is constructed based on these boundaries and a maximum value order statistics filter segments the Fourier spectrum with the adaptive decomposition of the signals. Finally, the envelope spectrum generated by CK is used to screen the bearing fault information, which belongs to the decomposition of a signal into empirical modes, so that the rolling bearing fault can be accurately diagnosed. The method’s effectiveness is verified by simulated signal experiments and rolling bearing fault signals. The results show that the performance of the proposed method in this paper is better than that of the traditional EWT. Therefore, the method can be applied to the field of bearing faults or other mechanical fault diagnosis directions.

Improving the robustness of spectral estimation to loud transients with a truncated order statistics filter

Underwater acoustic recordings often include loud transients from human or natural sources. The transients cause a positive bias for Welch's average periodogram spectral estimator when estimating the power spectral density of the background environment. Estimators based on single order statistics (e.g., the sample median) avoid the bias caused by outliers at the cost of a higher variance than the sample mean. Schwock and Abadi (2021) showed that, for exponential random variables, the estimator based on the 80th sample percentile has the lowest variance among any unbiased estimator based on a single order statistics. This work tests a hybrid approach between Welch's and order statistics estimators by performing a weighted sum of the quietest subset of ordered samples of the periodograms. By discarding the loudest samples of the periodogram, the truncated linear order statistics filter (TLOSF) reduces the bias caused by loud transients. By combining multiple order statistics into the estimate, the TLOSF achieves a lower variance than the 80th percentile estimator. The TLOSF reduced the MSE by 1dB compared to Schwock & Abadi's 80th percentile estimator for a mixture combining an exponential distribution with 1% outliers 23 dB above the background. On periodograms of shallow water hydrophone recordings, the TLOSF yielded a lower output power in the frequency bins where both the Welch's and 80th percentile estimators had a positive bias due to loud transients. [Work supported by ONR Code 321US.]

A nonlinear active noise control algorithm using the FEWT and channel-reduced recursive Chebyshev filter

Active noise control (ANC) has been widely studied to eliminate low-frequency noise. However, efficiently controlling higher-order distortions of nonlinear primary and secondary path is still a major challenge. To address this, this paper proposes a novel nonlinear ANC algorithm based on the fast empirical wavelet transform and recursive Chebyshev nonlinear filter. In this method, the fast empirical wavelet transform based on order-statistic filtering is first applied to decompose non-stationary noise into empirical mode functions (EMFs) which are more stationary and easy to control. Furthermore, a novel third-order Chebyshev nonlinear filter including the non-recursive subsection and recursive one is proposed to individually expand EMFs for compensating higher-order nonlinear distortions from primary path and secondary path. Moreover, the strategy of channel-reduced diagonal structure is designed to optimise the number of expanded channels, and the computational complexity of proposed algorithm is also investigated. Experimental results demonstrate that proposed method performs the highest noise reduction over the conventional algorithms but also has a fast convergence rate.

A cascade method for infrared dim target detection

Infrared dim target detection acts a pivotal role in searching and tracking applications. Due to the long-range distance, detection tasks are usually confronted with a low signal-to-noise ratio (SNR). To tackle the problem, a cascade method is proposed in this paper. Different from traditional gradient detection, the proposed method takes advantage of movement continuity to settle the pseudo targets elimination. Concisely, there are only three steps contained in cascade method. Initially, since some bad points might exist in the original infrared images, a local order-statistic filter is adopted to dispel pixel-sized fixed noise (PSFN). Secondly, processed infrared images are filtered by a 5 × 5 facet kernel to extract candidate targets from background. Finally, inspired by the movement continuity, a motion continuous pipeline (MCP) is built to achieve pseudo objects elimination. To measure the performance of the proposed method, a set of real infrared images (the SNR is around 1) covering different backgrounds are discussed in experiments. The results indicate that the proposed method outperforms conventional baseline methods in terms of detection rate and false-alarm.

Applications in bearing fault diagnosis of an improved Kurtogram algorithm based on flexible frequency slice wavelet transform filter bank

This paper proposes a flexible frequency slice wavelet transform (flexible FSWT) for Kurtogram, a classic signal processing method, with an intend to expand its range of application. The Kurtogram, however, does not consider the details of the spectrum while dividing the frequency bands, which may lead to diagnosis errors. The variable window characteristics of the order statistic filter and the minimum value spectrum segmentation method have been utilized to obtain the multi-level spectrum segmentation filter bank, which can be employed to construct the basic framework of the novel Kurtogram. Relying on the unrestricted filtering property of FSWT, the reconstruction and extraction of the composite spectrum boundaries have been realized. The flexible FSWT adds self-adaptability to the application of FSWT in fault diagnosis, and solves the problem of frequency band discrimination failure of time–frequency diagram diagnosis. The validity of flexible FSWT has been verified by simulation and experiment signals.

Feature extraction by enhanced analytical mode decomposition based on order statistics filter

The methods of mode decomposition based on the amplitude of spectrum are widely used in the fault diagnosis of bearings and gears in rotating machinery such as centrifuges, slurry pumps, fans, etc. Analytical mode decomposition with excellent filtering could set the bisecting frequency to distinguish useful modes. However, the vibration signal of equipment in actual operation is complex. This paper is devoted to the research of a novel spectral segmentation mode decomposition method. The proposed enhanced analytical mode decomposition takes advantage of the trend of spectrum fluctuations. In order to obtain the most critical bisecting frequency, the trend spectrum estimation method was proposed based on order statistics filter. The filtering effect of enhanced analytical mode decomposition was verified by the simulated signal. The experimental results show that the proposed method is efficient and the bearing inner and outer ring faults in the rotating machine can be successfully extracted.

A robust iris localization scheme for the iris recognition

Due to current security situations around the globe, iris biometric technology is highly preferred for both overt and covert applications. A typical iris biometric system includes image acquisition, iris segmentation, features extraction, and matching and recognition modules. Amongst these modules, iris segmentation plays a decisive role because it segments the valid iris part in an input eyeimage. It includes two tasks: iris localization and noise (e.g., eyelids) removal. Notably, the overall performance of an iris biometric system strongly relies on the iris localization task, because it demarcates the actual iris contours. Some contemporary iris localization schemes search over a three-dimensional (3D) space while marking iris boundaries, which is a time-consuming process if not optimized properly. Besides, some schemes also resort to the fixed and/or crude thresholding-based techniques for pupil localization. Notably, such schemes may perform poorly if image data do not maintain quality. To address these issues, this study proposes a robust iris localization scheme maintaining both speed and accuracy. It includes preprocessing the input eyeimage using an order statistic-filter and the bilinear interpolation scheme, extracting an adaptive threshold using the image’s histogram, processing binary image via the morphological operators, extracting pupil’s center and radius based on the centroid and geometry concepts, marking iris outer boundary using the Circular Hough transform (CHT) and refining coarse iris boundaries through the Fourier series. The proposed scheme exhibits relatively better experimental results compared with some contemporary iris localization schemes on the public iris databases: IITD V1.0, CASIA-Iris-Interval and MMU V1.0.

Quantum image mid-point filter

Mid-point filter is an order statistic filter which cannot be realized in the frequency domain. It is used for de-noising Gaussian noise effectively. In this paper, a new method for quantum realization mid-point filter in the spatial domain is proposed. An enhanced method for preparing multiple copies of the same image is also proposed. The modular design of the quantum circuit was utilized with an articulation on reducing the number of ancillary qubits. In this work, we present the quantum circuit for the three basic modules (cyclic shift, swap and division by two) and four composite modules (full adder, comparator, sort and maximum–minimum extraction). Also, the enhanced quantum preparation of multiple copies of an image is introduced. Moreover, the design of maximum–minimum extraction is modified to adapt our quantum circuit design. Finally, the complete quantum circuit which implements the mid-point filtering task is constructed and the results of several simulation experiments with different noise patterns are presented on some grayscale images. Apparently, the proposed approach has identical noise suppression of the classical version; however, there is a clear reduction in the complexity from exponential function of image size $$O(2^{2n})$$ to the second-order polynomial $$O(n^{2} + q)$$ .

Robust active contours driven by order-statistic filtering energy for fast image segmentation

In this paper, a robust active contour model driven by order-statistic filtering (OSF) energy is proposed for fast image segmentation. The main idea of the order-statistic filtering energy is to construct the edge force function (EFF) to quickly and adaptively attract curves to evolve towards the boundaries of targets. Besides, because the EFF is computed before iterations, therefore, segmentation speed of the OSF model improves greatly. Furthermore, an optimized regularization term and an optimized length term are used in the OSF model to replace the traditional penalty and length term, respectively. Experiments on some synthetic and real images show that the OSF model can segment images with intensity inhomogeneity quickly and precisely. In addition, several experiments also show that the OSF model is robust to initial contour and parameters.

Active contours driven by order-statistic filtering and coherence-enhancing diffusion filter for fast image segmentation

A robust active contour model driven by an order-statistic filtering and coherence-enhancing diffusion (OSFCED) filter for fast image segmentation is proposed. The main idea of the order-statistic filtering is to construct the edge force function (EFF) to quickly and adaptively attract evolving curves to target boundaries while a coherence-enhancing diffusion (CED) filter aims at filtering noise and enhancing target boundaries so that the segmentation efficiency can be improved. In addition, the computation of the EFF and CED function is completed before iterations. Therefore, the computational cost of the proposed model is low during curve evolution. Furthermore, the addition of optimized distance regularization term and optimized length term makes curve evolution smoother and more stable. Experiments performed show that the proposed model is robust to initial contour, parameter and has higher segmentation efficiency for images with intensity inhomogeneity.

Optimized LMD method and its applications in rolling bearing fault diagnosis

The local mean decomposition (LMD) method can adaptively decompose a vibration acceleration signal into a series of product functions with different frequency characteristics. However, in the process of calculating local mean and interpolation, this method not only increases the computational complexity, but also produces serious modal aliasing. In order to improve the computational speed and reduce modal aliasing, a new method is proposed to optimize local mean decomposition. The proposed method uses an order statistics filter to estimate the upper and lower envelopes of the signal. The moving average method is replaced by the envelope mean method to calculate the local mean function and envelope function. Subsequently, spectral negentropy is used as the stopping criterion of iteration and to filter the component which may contain fault information. Strict termination conditions in LMD are replaced. The invalid components avoid decomposition and the computational efficiency is improved. The dependence on extreme points is reduced, so the endpoint effect is suppressed. The experimental results show that the proposed method is capable of identifying bearing faults and is suitable for the diagnosis of composite faults of rolling bearings.

Application of fast singular spectrum decomposition method based on order statistic filter in rolling bearing fault diagnosis

Singular spectrum decomposition (SSD) is a new adaptive signal processing method for nonlinear and non-stationary signals. By constructing a trajectory matrix and adaptively selecting the embedding dimensions, the method divides non-stationary signals into several single-component signals successively from high frequency to low frequency. However, in the process of component reconstruction, bandwidth estimation and determining sizable trends by building a Gaussian function superposition spectral model are extremely complicated. Moreover, the parameter setting requires too much manual intervention and lacks theoretical support. Hence, aimed at nonlinear and non-stationary vibration signals of rolling bearings, a novel method of fault feature extraction based on the order statistic filter (OSF) for fast SSD (FSSD) is proposed. The FSSD method adopts the envelope method of OSFs to divide the spectrum and determine the sizable trend to improve the process. The proposed method is applied to bearing fault diagnosis. The analysis results of simulation signals and bearing experimental signals show that the new method can decompose signals quickly, effectively and accurately, and the mode mixing and time-consuming problems are refined.

Adaptive Kurtogram and its applications in rolling bearing fault diagnosis

Abstract As one of the most important components in the rotating machinery, the rolling bearing will affect the operation precision of the equipment, the running state of the gear, the degree of the axis and even cause the damage of the equipment. Therefore, it is very necessary to improve the processing methods of non-stationary signals. In this paper, an adaptive Kurtogram (AK) method is proposed. The greatest advantage of this method is the use of the order statistics filter (OSF) to estimate and divide the effective modal components from the spectrum to replace the fast Kurtogram (FK). The minimum envelope value of the signal in frequency domain is obtained and taken as the boundaries. Change the sliding window width to divide different boundaries and form an array. The empirical wavelet transform (EWT) is used to reconstruct the signal components according to the boundary array. Then their kurtosis values are calculated. The frequency band with the largest kurtosis value contains the impact information, and the corresponding time domain component presents periodicity impact. AK improves the shortcomings of the center frequency and the bandwidth of the fast Kurtogram (FK) that cannot be explained theoretically. The method of dividing the boundaries in the frequency domain is optimized. After verification by the simulated signals and the actual signals, this method is faster and more efficient.

A comparison between PCA and some enhancement filters for denoising astronomical images

This paper includes a comparison between denoising techniques by using statistical approach, principal component analysis with local pixel grouping (PCA-LPG), this procedure is iterated second time to further improve the denoising performance, and other enhancement filters were used. Like adaptive Wiener low pass-filter to a grayscale image that has been degraded by constant power additive noise, based on statistics estimated from a local neighborhood of each pixel. Performs Median filter of the input noisy image, each output pixel contains the Median value in the M-by-N neighborhood around the corresponding pixel in the input image, Gaussian low pass-filter and Order-statistic filter also be used.
 Experimental results shows LPG-PCA method gives better performance, especially in image fine structure preservation, compared with other general denoising algorithms.

Performance Analysis of Constant-False-Alarm-Rate Detectors Using Characteristic Functions

Constant-false-alarm-rate (CFAR) detectors in sonar and radar are often implemented by forming the ratio of an unnormalized decision statistic from a test cell to an estimate of the noise background power and comparing it to a decision threshold. Evaluation of the performance in terms of the detection and false alarm probabilities is traditionally done through the use of the probability density function (pdf) of the background power estimate and the cumulative distribution function (cdf) of the unnormalized test cell. An alternative approach is presented in this paper where the pdf, cdf, and other properties of the CFAR decision statistic are described as a function of the characteristic functions of the unnormalized test cell and the background power estimate. The characteristic-function-based approach is appealing because of its generally simpler form compared to the pdfs and cdfs of both the background power estimator and standard signal models (deterministic, Gaussian fluctuating, Rician, and gamma-fluctuating intensity). The technique is demonstrated through several examples including background power estimators formed using a weighted average (e.g., an exponential averager), an order-statistic filter, and correlated Gaussian data. The broad utility of the approach is illustrated by evaluating false alarm and detection performance of a cell-averaging normalizer for a significantly fluctuating signal in heavy-tailed clutter and by assessing how much nonstationarity in the background noise power is required for normalizing before incoherent integration to perform better than normalizing after.

Transform based image denoising

The Image denoising is the retrieval of quality image from the noisy image corrupted by channel noise at the time of transmission. Without denoising process it becomes very tough to carry further analysis on these types of images. In this paper, transform based image denoising techniques are proposed to address these issues for the removal of noise. The flow of work initiated with generation of sub-band coefficients using transform techniques like DCT, DWT, SWT etc. These coefficients are under goes spatial filtering process with order statistic filters like (min, max, median etc.) Then inverse transform is applied on the processes coefficients to generate denoised image. The resultant image is noiseless quality image and this can be used for further analysis.

Lymphoma images analysis using morphological and non-morphological descriptors for classification

Mantle cell lymphoma, follicular lymphoma and chronic lymphocytic leukemia are the principle subtypes of the non-Hodgkin lymphomas. The diversity of clinical presentations and the histopathological features have made diagnosis of such lymphomas a complex task for specialists. Computer aided diagnosis systems employ computational vision and image processing techniques, which contribute toward the detection, diagnosis and prognosis of digitised images of histological samples. Studies aimed at improving the understanding of morphological and non-morphological features for classification of lymphoma remain a challenge in this area. This work presents a new approach for the classification of information extracted from morphological and non-morphological features of nuclei of lymphoma images. We extracted data of the RGB model of the image and employed contrast limited adaptive histogram equalisation and 2D order-statistics filter methods to enhance the contrast and remove noise. The regions of interest were identified by the global thresholding method. The flood-fill and watershed techniques were used to remove the small false positive regions. The area, extent, perimeter, convex area, solidity, eccentricity, equivalent diameter, minor axis and major axis measurements were computed for the regions detected in the nuclei. In the feature selection stage, we applied the ANOVA, Ansari-Bradley and Wilcoxon rank sum methods. Finally, we employed the polynomial, support vector machine, random forest and decision tree classifiers in order to evaluate the performance of the proposed approach. The non-morphological features achieved higher AUC and AC values for all cases: the obtained rates were between 95% and 100%. These results are relevant, especially when we consider the difficulties of clinical practice in distinguishing the studied groups. The proposed approach is useful as an automated protocol for the diagnosis of lymphoma histological tissue.