Ridge Extraction Research Articles

Automatic identification of alternating morphological units in river channels using wavelet analysis and ridge extraction

Abstract. The accuracy of hydraulic models depends on the quality of the bathymetric data they are based on, whatever the scale at which they are applied. The along-stream (longitudinal) and cross-sectional geometry of natural rivers is known to vary at the scale of the hydrographic network (e.g., generally decreasing slope, increasing width in the downstream direction), allowing parameterizations of main cross-sectional parameters with large-scale proxies such as drainage area or bankfull discharge (an approach coined downstream hydraulic geometry, DHG). However, higher-frequency morphological variability (i.e., at river reach scale) is known to occur for many stream types, associated with varying flow conditions along a given reach, such as the alternate bars or the pool–riffle sequences and meanders. To consider this high-frequency variability of the geometry in the hydraulic models, a first step is to design robust methods to characterize the scales at which it occurs. In this paper, we introduce new wavelet analysis tools in the field of geomorphic analysis (namely, wavelet ridge extraction) to identify the pseudo-periodicity of alternating morphological units from a general point of view (focusing on pool–riffle sequences) for six small French rivers. This analysis can be performed on a single variable (univariate case) but also on multiple variables (multivariate case). In this study, we choose a set of four variables describing the flow degrees of freedom: velocity, hydraulic radius, bed shear stress, and a planform descriptor that quantifies the local deviation of the channel from its mean direction. Finally, this method is compared with the bedform differencing technique (BDT), by computing the mean, median, and standard deviation of their longitudinal spacings. The two methods show agreement in the estimation of the wavelength in all reaches except one. The method aims to extract a pseudo-periodicity of the alternating bedforms that allow objective identification of morphological units in a continuous approach with the maintenance of correlations between variables (i.e., at many station hydraulic geometry, AMHG) without the need to define a prior threshold for each variable to characterize the transition from one unit to another.

A Novel Fault Diagnosis Scheme for Rolling Bearing Based on Convex Optimization in Synchroextracting Chirplet Transform.

Synchroextracting transform (SET) developed from synchrosqueezing transform (SST) is a novel time-frequency (TF) analysis method. Its concentrated TF spectrum is obtained by applying a synchroextracting operator into TF transformation co-efficients on the TF plane. For this class of post-processing TF analysis methods, the main research focuses on the accurate estimation of instantaneous frequency (IF). However, the performance of TF analysis is greatly affected by the strong frequency modulation (FM) signal. In particular, the actual measured mechanical vibration signals always contain strong background noise, which decreases the resolution of TF representation, resulting in an inaccurate ridge extraction. To solve this problem, an improved penalty function based on the convex optimization scheme is firstly introduced for signal denoising. Based on the superiority of the linear chirplet transform (LCT) in dealing with modulated signals, the synchroextracting chirplet transform (SECT) is employed to sharpen the TF representation after the convex optimization denoising operation. To verify the effectiveness of the proposed method, the numerical simulation signals and the measured fault signals of rolling bearing are carried out, respectively. The results demonstrate that the proposed method leads to a better solution in rolling bearing fault feature extraction.

Ridge extraction based on adaptive variable-bandwidth cost functions by edge detection of time frequency images

Ridge extraction of a time frequency image (TFI) can serve to estimate an instantaneous frequency of a signal. However, there is a considerable difficulty in ridge extraction of a multi-ridge TFI due to mutual interference between ridges. Some traditional methods for ridge extraction fail to resolve this difficulty. The one-step cost function (OSCF), a typical method for processing a multi-ridge TFI, lacks self-adaptation in determining searching regions of a targeted ridge. To overcome this question, this paper proposes an adaptive variable-bandwidth cost function (AVBCF) for ridge extraction. Firstly, a TFI is acquired by time frequency analysis of a signal. Afterwards, the TFI is filtered into a binary image by a Canny detector. Also, some dispersive ridges in the binary image serve to form a synthetic dispersive ridge. Next, searching regions of a targeted ridge are estimated by projecting statistics of edges of the synthetic dispersive ridge to the targeted ridge. Next, the AVBCF is compared with the OSCF and some widespread methods numerally and experimentally. The results demonstrate that the AVBCF performs better than the other methods.

An Optimization Tendency Guiding Mode Decomposition Method for Bearing Fault Detection Under Varying Speed Conditions

Tacholess order tracking techniques based on time-frequency (TF) ridge detection have been extensively used in bearing fault diagnosis under varying speed conditions for decades. However, the signal components of a fault bearing related to shaft rotational frequency (SRF) is difficult to be accurately extracted by these methods because of TF resolution limitation and strong noise interference. A new TF decomposing algorithm, that is, variational nonlinear chirp mode decomposition (VNCMD) is effective to extract the time-varying feature under limited TF resolution. However, its performance is influenced by prior knowledge of initial parameters. Besides, ridge information hidden in noise is difficult to be mined effectively, which increases the difficulty of ridge extraction. In this study, a feature isolation technology is proposed to enhance fault-related features and reduce the interference of noise and irrelevant components. Then inspired by the decomposing properties research on the convergence characteristics of VNCMD, an optimization tendency guiding mode decomposition (OTGMD) method is proposed to track the instantaneous frequency (IF) of fault-related mode, which can alleviate the personnel experience requirement and is not affected by the set of TF resolution. The proposed method mainly consists of three steps. First, SRF-related information is highlighted through low-pass filtering, and the dominant IF is achieved through ridge detection method. Subsequently, for the convenience of mode extraction, the fault characteristic is augmented through iterative envelope analysis. Then, the OTGMD optimization strategy is developed to gradually decompose the target mode on the basis of the above process. Finally, a stopping criterion based on characteristic frequency ratios (CFRs) is constructed to adaptively terminate the iteration process. Simulation and experiments demonstrate that the proposed method is effective and suitable for bearing fault diagnosis under varying speed conditions.

A hybrid method of multi-objective particle swarm optimization and k-means clustering and its application to modal parameter estimation in the time–frequency domain

Modal parameters provide an insight into the dynamical properties of structures. In the time–frequency domain–based methods, time–frequency ridges contain crucial information on the characteristics of multicomponent signals, and manually extracting time–frequency ridges is a huge burden, especially when long-time time-varying modal parameters are focused on. In this study, time–frequency ridge extraction is converted into a multi-objective optimization problem, and a new hybrid method of multi-objective particle swarm optimization and k-means clustering is proposed to solve such a multi-objective optimization problem. In the hybrid method, the particle swarm is partitioned into sub-swarms by k-means clustering, and the sub-swarms are used to search new solutions for updating a finite-sized external archive, which is used as the exclusive centroids of the k-means clustering. Simultaneously, the finite-sized external archive serves as global best positions of sub-swarms. Both simulated and experimental cases are applied to validate the hybrid method. With the aid of the hybrid method, the influence of varying temperatures on modal parameters of a column beam is experimentally analyzed in detail.

An objective-adaptive refinement criterion based on modified ridge extraction method for finite-time Lyapunov exponent (FTLE) calculation

High-accuracy and high-efficiency finite-time Lyapunov exponent (FTLE) calculation method has long been a research hot point, and adaptive refinement method is a kind of method in this field. The proposed objective-adaptive refinement (OAR) criterion can put adaptive particles at the vicinity of FTLE ridges. The FTLE ridge is extracted not simply by the magnitude of FTLE (would cause false negative refinement) and error (would cause false positive refinement) but by a modified gradient climbing method. Moreover, the refinement regions converge to some certain region because of the objectivity of the refinement region.

Time Frequency Representation Enhancement via Frequency Matching Linear Transform for Bearing Condition Monitoring under Variable Speeds

Instantaneous frequency (IF) of shaft rotation is pivotal for bearing fault diagnosis under variable speed operations. However, shaft IF cannot always be measured as tachometers are not allowed to be installed in every case due to design reasons and cost concerns. Extracting the shaft IF ridge from time frequency representation (TFR) of vibration signals, therefore, becomes an alternative. Linear transform (LT), such as short time Fourier transform (STFT), has been widely adopted for such a purpose. Nevertheless, the accuracy of extracted IF ridges relies on the readability of TFR. Unfortunately, readability of TFR from STFT is often impaired by the smearing effect caused by non-synchronous frequencies between bases and signal components and limited time frequency resolution capability, which in turn adversely influences the accuracy of IF ridge extraction. To accurately extract IF ridges from vibration signals, this paper focuses on the first factor, which causes the smearing problem, and proposes a method named frequency matching linear transform (FMLT) to enhance the TFR, where transforming bases with frequencies varying with the shaft IF are constructed to alleviate the smearing effects. To construct the transforming bases with frequencies synchronous with shaft IF, a fast path optimization (FPO) algorithm, which generates all possible optimization paths among amplitude peaks and thereby ensures the continuity of extracted IF ridges, is adopted for IF pre-estimation. The TFR with improved readability can be subsequently obtained via FMLT, paving the way for accurate IF ridge extraction. Then, multiple IF ridges can be iteratively extracted using the FPO algorithm. The accuracy of extracted IF ridges before and after TFR enhancement is compared, indicating that the proposed FMLT can enhance the readability of TFR and lead to more accurate IF ridge extraction for bearing condition monitoring.

Lamb Wave Mode Decomposition Based on Cross-Wigner-Ville Distribution and Its Application to Anomaly Imaging for Structural Health Monitoring.

Lamb waves are characterized by their multimodal and dispersive propagation, which often complicates analysis. This paper presents a method for separation of the mode components and reflected components in sensor signals in an active structural health monitoring (SHM) system. The system is trained using linear chirp signals but works for arbitrary excitation signals. The training process employs the cross-Wigner-Ville distribution (xWVD) of the excitation signal and the sensor signal to separate the temporally overlapped modes in the time-frequency domain. The mode decomposition method uses a ridge extraction algorithm to separate each signal component in the time-frequency distribution. Once the individual modes are separated in the time-frequency domain, they are reconstructed in the time domain using the inverse xWVD operation. The propagation impulse response associated with each component can be directly estimated for chirp inputs. The estimated propagation impulse response can be used to separate the modes resulting from arbitrary excitation signals as long as their frequency components fall in the range of the chirp signal. The usefulness of the mode decomposition algorithm is demonstrated on a new health monitoring system for composite structures. This system performs anomaly imaging using the first arriving mode extracted from sensor array signals acquired from the structure. The anomaly maps are computed using a sparse tomographic reconstruction algorithm. The reconstructed map can locate anomalies on the structure and estimate their boundaries. Comparisons with methods that do not employ mode decomposition and/or sparse reconstruction techniques indicate a substantially better performance for the method of this paper.

Whale Vocalization Classification Using Feature Extraction With Resonance Sparse Signal Decomposition and Ridge Extraction

Whales communicate using whistle vocalizations that are essentially underwater acoustic frequency-modulated tones. Inevitable environmental noise decreases recognition accuracy of these sounds during wide range detection. In this paper, we propose a robust time – frequency analysis method that combines resonance sparse signal decomposition (RSSD) and spectrogram ridge extraction. We apply RSSD to extract whistle components from the raw signal, and then we segment the ridge regions of the whistle spectrograms. By applying a partial derivative method, we extract the whistle spectrogram ridge representing an accurate trace of the whistle vocalization. From these results, we extract ridge features and use an SVM or a random forest to identify the whale species. We evaluated our method using experiments with samples for four whale species. Compared with direct ridge extraction directly without RSSD, our proposed method achieved better extraction of frequency characteristics of the vocalizations. Our proposed method achieved an accuracy rate of over 98% for sounds from four species when using five training samples.

Order spectrogram visualization for rolling bearing fault detection under speed variation conditions

Abstract For rotating machinery condition monitoring and fault diagnosis under speed variation conditions, order tracking has been considered as a very powerful non-stationary vibration signal analysis method, when compared with the frequency analysis methods based on stationary assumption. However, the conventional order tracking methods require additional hardware to provide a phase reference signal. This constraint limits the conventional methods in industrial applications significantly. In order to further improve the applicability of the conventional order tracking methods, some tacho-less order tracking methods have been proposed in the past few years. Despite the tacho-less order tracking methods successfully getting rid of reference signal, the algorithms are very complex and the computational burden is increased correspondingly. To address the aforementioned shortcomings, a straightforward tacho-less order tracking method based on order spectrogram visualization is proposed in this paper. In the proposed method, a ridge extraction approach is used to estimate the instantaneous frequency of a certain rotating frequency harmonic. And then the vibration signal is resonance demodulated and the time-frequency distribution of the demodulated signal is obtained. A subsequent transform is conducted and the frequency axis of the time-frequency distribution is rescaled based on the estimated instantaneous frequency of rotating shaft. Then, an order spectrogram is constructed and thereby the non-stationary interference introduced by rotating speed fluctuation is suppressed. Finally, fault orders are uncovered and bearing fault type can be identified. The effectiveness of the proposed method has been validated by both simulated and experimental rolling bearing vibration signals. The results illustrate the improved features regarding previously developed tacho-less order tracking method in bearing diagnosis under speed variation conditions.

THE COMPARISON OF DRAINAGE NETWORK EXTRACTION BETWEEN SQUARE AND HEXAGONAL GRID-BASED DEM

Abstract. The automatic extraction of valleys or ridges from DEM is a long term topic in the GIS and hydrology fields and a number of algorithms have been developed. The quality of drainage networks extraction depends on many impacts such as data source, DEM resolution and extraction algorithms. However, little consideration has been paid to the influence of different tessellation of grid-based DEM construction in terrain surface representation. Actually, hexagonal grid has been proved to be advantageous over square grid due to its consistent connectivity, isotropy of local neighbourhoods, higher symmetry, visual advantage, and so on. This study tries to explore the impact of different tessellation scheme for grid-based DEM on the accuracy of terrain representation reflected by the results of drainage networks extraction. The contour line data model is applied to grid-based DEM generation. Then, by analogy with traditional D8 algorithm, the D6 algorithm is introduced to extract drainage networks by calculating flow direction of each gird with the steepest slope neighbour criteria. From the comparison between D8 algorithm and D6 algorithm, we conclude that hexagonal grid-based DEM has a superior capability in maintaining the detailed shape and the characteristics of extracted drainage networks in coarser resolution.

Investigation on Planetary Bearing Weak Fault Diagnosis Based on a Fault Model and Improved Wavelet Ridge

Rolling element bearings are of great importance in planetary gearboxes. Monitoring their operation state is the key to keep the whole machine running normally. It is not enough to just apply traditional fault diagnosis methods to detect the running condition of rotating machinery when weak faults occur. It is because of the complexity of the planetary gearbox structure. In addition, its running state is unstable due to the effects of the wind speed and external disturbances. In this paper, a signal model is established to simulate the vibration data collected by sensors in the event of a failure occurred in the planetary bearings, which is very useful for fault mechanism research. Furthermore, an improved wavelet scalogram method is proposed to identify weak impact features of planetary bearings. The proposed method is based on time-frequency distribution reassignment and synchronous averaging. The synchronous averaging is performed for reassignment of the wavelet scale spectrum to improve its time-frequency resolution. After that, wavelet ridge extraction is carried out to reveal the relationship between this time-frequency distribution and characteristic information, which is helpful to extract characteristic frequencies after the improved wavelet scalogram highlights the impact features of rolling element bearing weak fault detection. The effectiveness of the proposed method for weak fault recognition is validated by using simulation signals and test signals.

A wavelet ridge extraction method employing a novel cost function in two-dimensional wavelet transform profilometry

We present a new wavelet ridge extraction method employing a novel cost function in two-dimensional wavelet transform profilometry (2-D WTP). First of all, the maximum value point is extracted from two-dimensional wavelet transform coefficient modulus, and the local extreme value points over 90% of maximum value are also obtained, they both constitute wavelet ridge candidates. Then, the gradient of rotate factor is introduced into the Abid’s cost function, and the logarithmic Logistic model is used to adjust and improve the cost function weights so as to obtain more reasonable value estimation. At last, the dynamic programming method is used to accurately find the optimal wavelet ridge, and the wrapped phase can be obtained by extracting the phase at the ridge. Its advantage is that, the fringe pattern with low signal-to-noise ratio can be demodulated accurately, and its noise immunity will be better. Meanwhile, only one fringe pattern is needed to projected to measured object, so dynamic three-dimensional (3-D) measurement in harsh environment can be realized. Computer simulation and experimental results show that, for the fringe pattern with noise pollution, the 3-D surface recovery accuracy by the proposed algorithm is increased. In addition, the demodulation phase accuracy of Morlet, Fan and Cauchy mother wavelets are compared.

An adaptive and tacholess order analysis method based on enhanced empirical wavelet transform for fault detection of bearings with varying speeds

The order tracking method based on time-frequency representation is regarded as an effective tool for fault detection of bearings with varying rotating speeds. In the traditional order tracking methods, a tachometer is required to obtain the instantaneous speed which is hardly satisfied in practice due to the technical and economical limitations. Some tacholess order tracking methods have been developed in recent years. In these methods, the instantaneous frequency ridge extraction is one of the most important parts. However, the current ridge extraction methods are sensitive to noise and may easily get trapped in a local optimum. Due to the presence of noise and other unrelated components of the signal, bearing fault features are difficult to be detected from the envelope spectrum or envelope order spectrum. To overcome the abovementioned drawbacks, an adaptive and tacholess order analysis method is proposed in this paper. In this method, a novel ridge extraction algorithm based on dynamic path optimization is adopted to estimate the instantaneous frequency. This algorithm can overcome the shortcomings of the current ridge extraction algorithms. Meanwhile, the enhanced empirical wavelet transform (EEWT) algorithm is applied to extract the bearing fault features. Both simulated and experimental results demonstrate that the proposed method is robust to noise and effective for bearing fault detection under variable speed conditions.

Visualization of fracture progression in peridynamics

We present a novel approach for the visualization of fracture processes in peridynamics simulations. In peridynamics simulation, materials are represented by material points linked with bonds, providing complex fracture behavior. Our approach first extracts the cracks from each time step by means of height ridge extraction. To avoid deterioration of the structures, we propose an approach to extract ridges from these data without resampling. The extracted crack geometries are then combined into a spatiotemporal structure, with special focus on temporal coherence and robustness. We then show how this structure can be used for various visualization approaches to reveal fracture dynamics, with a focus on physical mechanisms. We evaluate our approach and demonstrate its utility by means of different data sets.

On Demodulation, Ridge Detection, and Synchrosqueezing for Multicomponent Signals

In this paper, we present a novel technique for the retrieval of the modes of a multicomponent signal using a time-frequency (TF) representation of the signal. Our approach is based on a novel ridge extraction method that takes into account the fact that the TF representation is both discrete in time and frequency, followed by a demodulation procedure. Numerical results show the benefits of the proposed approach for mode reconstruction in comparison to similar techniques that do not make use of demodulation. Furthermore, numerical investigations show that the proposed approach sharpens the TF representation on which it is built.

Modal identification using the frequency-scale domain decomposition technique of ambient vibration responses

This paper proposes a new modal identification method of ambient vibration responses. The application of the singular value decomposition to continuous wavelet transform of power spectral density matrix gives singular values and singular vectors in frequency-scale domain. Analytical development shows a direct relation between local maxima in frequency-scale representation of singular values and modal parameters. This relation is then carried on for the identification of modal parameters via a complete practical procedure. The main novelties of this work involve the new formulation in frequency-scale domain and the capacity for the identification of modal parameters without the step of ridges extraction in comparison with previous wavelet-based modal identification methods.

Adaptive multimode signal reconstruction from time-frequency representations.

This paper discusses methods for the adaptive reconstruction of the modes of multicomponent AM–FM signals by their time–frequency (TF) representation derived from their short-time Fourier transform (STFT). The STFT of an AM–FM component or mode spreads the information relative to that mode in the TF plane around curves commonly called ridges. An alternative view is to consider a mode as a particular TF domain termed a basin of attraction. Here we discuss two new approaches to mode reconstruction. The first determines the ridge associated with a mode by considering the location where the direction of the reassignment vector sharply changes, the technique used to determine the basin of attraction being directly derived from that used for ridge extraction. A second uses the fact that the STFT of a signal is fully characterized by its zeros (and then the particular distribution of these zeros for Gaussian noise) to deduce an algorithm to compute the mode domains. For both techniques, mode reconstruction is then carried out by simply integrating the information inside these basins of attraction or domains.

基于评价函数的二维小波变换轮廓术小波脊提取方法

Wavelet ridge extraction is a key step in the wavelet transform profilometry. The speed and noise suppression capability of the wavelet ridge extraction method directly influences the wavelet transform profilometry. One new wavelet ridge extraction method used in the two-dimensional wavelet transform profilometry is proposed based on a new evaluation function. This function is established by using the module information from the wavelet transform coefficients, fringe instantaneous frequency and local fringe direction to improve the noise suppression capability. Moreover, one fast dynamic optimization algorithm is adopted to improve the wavelet ridge extraction speed. Computer simulation and experimental demonstration verify the proposed method's effectiveness.

Rolling element bearing defect detection using the generalized synchrosqueezing transform guided by time–frequency ridge enhancement

Healthy rolling element bearings are vital guarantees for safe operation of the rotating machinery. Time–frequency (TF) signal analysis is an effective tool to detect bearing defects under time-varying shaft speed condition. However, it is a challenging work dealing with defective characteristic frequency and rotation frequency simultaneously without a tachometer. For this reason, a technique using the generalized synchrosqueezing transform (GST) guided by enhanced TF ridge extraction is suggested to detect the existence of the bearing defects. The low frequency band and the resonance band are first chopped from the Fourier spectrum of the bearing vibration measurements. The TF information of the lower band component and the resonance band envelope are represented using short-time Fourier transform, where the TF ridge are extracted by harmonic summation search and ridge candidate fusion operations. The inverse of the extracted TF ridge is subsequently used to guide the GST mapping the chirped TF representation to the constant one. The rectified TF pictures are then synchrosqueezed as sharper spectra where the rotation frequency and the defective characteristic frequency can be identified, respectively. Both simulated and experimental signals were used to evaluate the present technique. The results validate the effectiveness of the suggested technique for the bearing defect detection.