Kaiser Energy Research Articles

A New Method of Two-stage Planetary Gearbox Fault Detection Based on Multi-Sensor Information Fusion

Due to their high transmission ratio, high load carrying capacity and small size, planetary gears are widely used in the transmission systems of wind turbines. The planetary gearbox is the core of the transmission system of a wind turbine, but because of its special structure and complex internal and external excitation, the vibration signal spectrum shows strong nonlinearity, asymmetry and time variation, which brings great trouble to planetary gear fault diagnosis. The traditional time-frequency analysis technology is insufficient in the condition monitoring and fault diagnosis of wind turbines. For this reason, we propose a new method of planetary gearbox fault diagnosis based on Compressive sensing, Two-dimensional variational mode decomposition (2D-VMD) and full-vector spectrum technology. Firstly, the nonlinear reconstruction and noise reduction of the signal is carried out by using compressed sensing, and then the signal with multiple degrees of freedom is adaptively decomposed into multiple sets of characteristic scale components by using 2D-VMD. Then, Rényi entropy is used as the optimization index of 2D-VMD analysis performance to extract the effective target intrinsic mode function (IMF) component, reconstruct the dynamics signal in the planetary gearbox, and improve the signal-to-noise ratio. Then, using the full-vector spectrum technique, the homologous information collected by numerous sensors is data layer fused in the spatial domain and the time domain to increase the comprehensiveness and certainty of the fault information. Finally, the Teager–Kaiser energy operator is used to demodulate the potential low-frequency dynamics frequency characteristics from the high-frequency domain and detect the fault characteristic frequency. Furthermore, the correctness and validity of the method are verified by the fault test signal of the planetary gearbox.

Modulation Sideband Separation Using the Teager–Kaiser Energy Operator for Rotor Fault Diagnostics of Induction Motors

Broken rotor bar (BRB) faults are one of the most common faults in induction motors (IM). One or more broken bars can reduce the performance and efficiency of the IM and hence waste the electrical power and decrease the reliability of the whole mechanical system. This paper proposes an effective fault diagnosis method using the Teager–Kaiser energy operator (TKEO) for BRB faults detection based on the motor current signal analysis (MCSA). The TKEO is investigated and applied to remove the main supply component of the motor current for accurate fault feature extraction, especially for an IM operating at low load with low slip. Through sensing the estimation of the instantaneous amplitude (IA) and instantaneous frequency (IF) of the motor current signal using TKEO, the fault characteristic frequencies can be enhanced and extracted for the accurate detection of BRB fault severities under different operating conditions. The proposed method has been validated by simulation and experimental studies that tested the IMs with different BRB fault severities to consider the effectiveness of the proposed method. The obtained results are compared with those obtained using the conventional envelope analysis methods and showed that the proposed method provides more accurate fault diagnosis results and can distinguish the BRB fault types and severities effectively, especially for operating conditions with low loads.

Selected Rolling Bearing Fault Diagnostic Methods in Wheel Embedded Permanent Magnet Brushless Direct Current Motors

In recent years, the number of outer rotor permanent magnet brushless direct current (PM BLDC) motor drives has been intensively growing. Due to the specifics of drive operation, bearing faults are especially common, which results in motor stoppage. In a number of these types of motor applications, the monitoring and diagnostics of bearing conditions is relatively rare. This article presents the results of research aimed at searching for simple and simultaneously effective methods for assessing the condition of bearings that can be built into the drive control system. In the experimental research, four vibration signal processing methods were analysed with regards to the identification accuracy of fault symptoms in the geometric elements of bearings (characteristic frequencies). The results are presented for three cases of bearing faults and compared with a new bearing, they were obtained based on a vibration signal analysis using the classical fast Fourier transform (FFT), Fourier transform of signal absolute values, Fourier transform of an envelope signal obtained using the Hilbert transform, and the Fourier transform of a signal filtered with the Teager–Kaiser energy operator (TKEO).

High Impedance Fault Detection Method Based on Variational Mode Decomposition and Teager–Kaiser Energy Operators for Distribution Network

The focus of the paper is the difficulty of high impedance fault (HIF) detection in distribution network, and its ease to be confused with capacitor switching (CS) and load switching (LS). Based on the intermittent reignition and extinction characteristics of HIF current, this paper proposes a novel HIF detection method, which combines variational mode decomposition (VMD) and Teager–Kaiser energy operators (TKEOs). The HIF detection method is as follows: First, perform the VMD on transient zero sequence currents to obtain the intrinsic mode functions (IMFs) and select the IMFs with the largest kurtosis value as the characteristic IMFs. Second, calculate the characteristic IMFs to obtain TKEOs and divide into subintervals of TKEOs waveform to calculate the time entropy values. Finally, construct HIF detection criterion as follows: when time entropy value is 0, it is judged as CS or LS. When the entropy value is not 0, it is judged as HIF. A large number of simulations and field data tests show that the method is accurate and stable, and under the interference of 1 dB strong noise, it can accurately judge. Compared with other methods, the method has higher feature extraction accuracy, less calculation time, and better judgment accuracy.

Gear fault diagnosis under non-stationary operating mode based on EMD, TKEO, and Shock Detector

Condition monitoring of gearboxes running under non-stationary operating conditions is a very difficult task. In this study, a signal processing technique is developed for damage detection of a bevel gearbox running under variable load and speed conditions. The proposed technique is applied on simulated vibration data computed through a dynamic model of bevel gearbox. The procedure used in this technique is based on the extraction of the shock related to the defect using the Shock Detector (SD) method. Firstly, vibration signals are decomposed into IMFs using Empirical Mode Decomposition (EMD). Then, the Teager–Kaiser Energy Operator (TKEO) is used to assess the instantaneous energy of the signal. Afterwards, SD is applied to examine and quantify the shock contents of the TKEO signal, which reflect the effect of the defect.

Rolling Element Bearing Fault Diagnosis Based on Adaptive Local Iterative Filtering Decomposition and Teager–Kaiser Energy Operator

The fault feature of rolling element bearings in early failure period is so weak and susceptible to random noise that it is very difficult to be extracted, so combined adaptive local iterative filtering decomposition (ALIFD) with Teager–Kaiser energy operator (TKEO) for rolling element bearings fault diagnosis. This experiment provides access to bearing test data for faulty bearings, and acceleration data was measured at locations near the bearings. The results show that this method can be used to accurately extract different frequency components of bearing fault vibration signals and diagnose bearing fault location.

Gait Event Detection From Accelerometry Using the Teager-Kaiser Energy Operator.

A novel method based on the application of the Teager-Kaiser Energy Operator is presented to estimate instances of initial contact (IC) and final contact (FC) from accelerometry during gait. The performance of the proposed method was evaluated against four existing gait event detection (GED) methods under three walking conditions designed to capture the variance of gait in real-world environments. A symmetric discrete approximation of the Teager-Kaiser energy operator was used to capture simultaneous amplitude and frequency modulations of the shank acceleration signal at IC and FC during flat treadmill walking, inclined treadmill walking, and flat indoor walking. Accuracy of estimated gait events were determined relative to gait events detected using force-sensitive resistors. The performance of the proposed algorithm was assessed against four established methods by comparing mean-absolute error, sensitivity, precision, and F1-score values. The proposed method demonstrated high accuracy for GED in all walking conditions, yielding higher F1-scores (IC: >0.98, FC: >0.9) and lower mean-absolute errors (IC: <0.018s, FC: <0.039s) than other methods examined. Estimated ICs from shank-based methods tended to exhibit unimodal distributions preceding the force-sensitive resistor estimated ICs, whereas estimated gait events for waist-based methods had quasiuniform random distributions and lower accuracy. Compared with the established gait event detection methods, the proposed method yielded comparably high accuracy for IC detection, and was more accurate than all other methods examined for FC detection. The results support the use of the Teager-Kaiser Energy Operator for accurate automated GED across a range of walking conditions.

Real-Time Multiple Event Detection and Classification in Power System Using Signal Energy Transformations

Real-time multiple event analysis is important for reliable situational awareness and secure operation of the power system. Multiple sequential events can induce complex superimposed pattern in the data and are challenging to analyze in real time. This paper proposes a method for accurate detection, temporal localization, and classification of multiple events in real time using synchrophasor data. For detection and temporal localization, a Teager–Kaiser energy operator (TKEO) based method is proposed. For event classification, a time series classification based method using energy similarity measure (ESM) is proposed. The proposed method is tested for simulated multiple event cases in the IEEE-118 bus system using DigSilent/PowerFactory and real PMU data for the Indian grid.

Application of TKEO in the process of automatic balancing of the rotor

The article presents an example of application of the Teager-Kaiser Energy Operator in automatic rotor balancing. The Teagear Kaiser Energy Operator is a signal analysis method, which allows for some mechanical objects to estimate energy changes in Newtonian terms by means of a displacement signal. Rotors are a structural element that rotates around an axis. Traditional balancing of the rotors is based on the introduction of correction masses, the aim of which is to reduce vibrations and noise during machine operation. Traditional balancing of the rotors is also possible. It can be realized by a system of correction masses with variable distance from the axis of rotation. The change of the correction mass distance from the axis of rotation influences the change of inertia of the object and thus reduces the unbalance. Depending on the design of the device, the modernization may assume extension or replacement of individual elements. Improvement of the operation of the device requires selection of elements depending on the overall interference in the operation of the machine and the impact on the operation of the entire device. The presented original method of automatic unbalance control with the use of the Energy Operator with the selection of parameters has been performed on a real laboratory stand..

Fault detection for PV systems using Teager–Kaiser energy operator

Owing to economical and environmental concerns, the photovoltaic (PV) technology has been significantly developed over the past few years. To ensure the safe operation of PV systems, it is necessary to develop effective fault detection techniques. Low-fault current of high-impedance, low-mismatch, and low-irradiance faults may lead to they remain undetected, resulting in potential fire hazard and energy loss. The use of blocking diodes and operation of maximum power point tracking algorithm increase the difficulty of PV fault detection. Using the Teager–Kaiser energy operator, a novel index to detect the challenging PV fault conditions without any prior information about the PV array and the training data set is proposed. The proposed index can differentiate the string-to-ground, string-to-string, and open-circuit faults from partial shadings in both grid-connected and islanded modes of operations. Simulation results in MATLAB/Simulink environment validate the performance of the proposed fault detection index.

A Teager–Kaiser Energy Operator and Wavelet Packet Transform for Bearing Fault Detection

The excellent features of bearing vibration signal are gainful to make accurate diagnosis results on the type of bearing damage. In this paper, a signal analysis technique based on wavelet packet transform (WPT) and Teager–Kaiser energy operator (TKEO) are presented. The objective of the proposed method is to demonstrate the effectiveness of the statistical parameters as the principal criterion for selecting the optimal frequency band in order to extract fault characteristics from vibration signal. Then, the TKEO is employed to track the modulation energy. The simulation and experimental results indicate that the proposed method enhances performances for detecting the bearing faults.

Teager–Kaiser energy methods for signal and image analysis: A review

This paper provides a review of the Teager–Kaiser (TK) energy operator and its extensions for signals and images processing. This class of operators possesses simplicity and good time-resolution and is very efficient in instantaneously estimating AM–FM signals and images. We point out the importance of the concept of energy from the point of view of the generation of the signal. More precisely, we emphasize the importance of analyzing signals from the point of view of the energy of the system needed to produce them. We show how this class of TK energy operators can be used to estimate useful features for signals and images analysis in time, space and frequency domains such as instantaneous frequency, second-order moment frequency, coherence function or spatial envelope and phase. We also show the importance of the higher derivative order of TK energy operator in terms of demodulation for both mono and multi-dimensional signals. Most of the developed tools around TK energy operators deal with real and complex-valued signals and some of them extended to multi-dimensional case. Due to their low complexity and their instantaneous-adapting nature, the class of TK energy operators offers valuable processing tools for time (space), frequency and time–frequency analysis.

Fault Diagnosis Method for Rolling Element Bearings Under Variable Speed Based on TKEO and Fast-SC

With rotating speed of rotating machinery, it is difficult to maintain stability in practical work which brings many difficulties to the condition monitoring of rotating machinery. When rolling element bearings work under variable speed, the corresponding vibration will contain obvious non-stationary characteristics, along with the presence of strong background noise, which makes it difficult for some traditional spectrum analysis methods to identify the characteristic frequency of bearings fault. In spite of the existence of strong non-stationary characteristics, the bearing fault signal has some hidden periodic components in the angle domain which makes it possible to extract the fault feature of bearings by means of spectral correlation analysis. Therefore, a fault feature extraction method based on Teager–Kaiser energy operator (TKEO) and fast spectral correlation (Fast-SC) in angle domain is proposed in this paper; Fast-SC is a newly proposed spectral correlation calculation method which can effectively improve the efficiency of computing; Teager–Kaiser energy operator can enhance the transient impact which also has a fast computing speed. In this paper, the instantaneous speed of each time is estimated by the time–frequency analysis method based on short-time Fourier transform and then, the original time-domain signal is resampled in angle domain; the TKEO is used to strengthen the fault impact components in signal; finally, the Fast-SC is applied to the strengthened signals, the enhanced envelope spectrum is calculated, and the fault features of rolling bearings are extracted. The effectiveness of the method is verified by measured signals.

A new fault diagnosis method based on deep belief network and support vector machine with Teager–Kaiser energy operator for bearings

How to improve the accuracy and algorithm efficiency of bearing fault diagnosis has been the focus and hot topic in fault diagnosis field. Deep belief network is a typical deep learning method, which can be used to form a much higher-level abstract representation and find the distributed characteristics of data. In this article, a new method of bearing fault diagnosis is proposed based on Teager–Kaiser energy operator and the particle swarm optimization-support vector machine with deep belief network. In this method, the demodulation signal is obtained using Teager–Kaiser energy operator first. And then the time and frequency statistic characteristic of the demodulation signal is analyzed. Furthermore, the deep belief network is used to extract time and frequency feature extraction. Finally, the extracted parameters are classified by particle swarm optimization-support vector machine. The experimental results show that it not only has higher accuracy but also shortens the training time greatly, and it improves the accuracy and efficiency of fault diagnosis obviously.

An alternative demodulation method using envelope-derivative operator for bearing fault diagnosis of the vibrating screen

The Teager–Kaiser energy operator (TKEO) and Hilbert transform (HT) are widely used as conventional demodulation methods in the signal processing field; however, it is well known that they are sensitive to vibration interference and noise, and these limitations hamper their applications, especially in the presence of strong noise. A vibrating screen is a kind of screening equipment in the field of vibrating machinery, which differs greatly from the rotating machinery in terms of structural characteristics and operational principles. The vibration signal extracted from the vibrating screen is not only comprised of multiple constituents but also a great deal of background noise. Thus, TKEO and HT have a large limitation on bearing fault diagnosis of the vibrating screen. To overcome these shortcomings, an alternative energy operator method named the envelope-derivative operator (EDO) is proposed. The results of simulation and bearing fault diagnosis of the vibrating screen indicate that EDO can effectively extract fault characteristic frequency, certifying its feasibility and superiority in comparison with TKEO and EDO.

Wiener Teager–Kaiser energy method for phase derivative estimation: application to speckle interferometry

We present a Wiener Teager–Kaiser approach for phase derivative estimation from a single speckle correlation fringe. In principle, the Teager–Kaiser operator estimates the energy of the fringe pattern and extracts its phase derivatives using an energy separation algorithm. However, in the estimation of the energy, this operator presents a computation error mainly due to a high frequency component. In this work, we addressed this error in mean square error sense by applying the Wiener filter on the operator prior to phase derivative computation. The performance of our proposed method on simulated and real fringe improves significantly the accuracy of the Teager–Kaiser operator.

Hybrid data fusion approach for fault diagnosis of fixed-axis gearbox

Intelligent fault diagnosis system based on condition monitoring is expected to assist in the prevention of machine failures and enhance the reliability with lower maintenance cost. Most machine breakdowns related to gears are a result of improper operating conditions and loading, hence leads to failure of the whole mechanism. With advancement in technology, various gear fault diagnosis techniques have been reported which primarily focus on vibration analysis with statistical measures. However, acoustic signals posses a huge potential to monitor the status of the machine but a few studies have been carried out till now. This article describes the implementation of Teager–Kaiser energy operator and empirical mode decomposition methods for fault diagnosis of the gears using acoustic and vibration signals by extracting statistical features. A cross-correlation-based fault index that assists the automatic selection of the sensitive Intrinsic Mode Function (IMF) containing fault information has also been described. The features extracted by all combinations of signal processing techniques are sorted by order of relevance using floating forward selection method. The effectiveness is demonstrated using the results obtained from the experiments. The fault diagnosis is performed with k-nearest neighbor classifier. The results show that the hybrid of empirical mode decomposition–Teager–Kaiser energy operator techniques employs the advantages traits of one or the other technique to generate overall improvement in diagnosing severity of local faults.

Identification method for power system low‐frequency oscillations based on improved VMD and Teager–Kaiser energy operator

An improved variational mode decomposition (VMD) method is introduced into the mode recognition of low-frequency oscillation of power system in this study. First, fast Fourier transform is used to determine the number of VMD components, and the approximate fitting formula of the best balancing parameter α is obtained by a large number of tests. The original signal is decomposed into several modes via improved VMD (IMVD) method. Then, Teager–Kaiser energy operator is applied on the fitting of each component to get the amplitude, frequency, and damping factor of it. By the constructed test signals, the proposed method is compared with the methods of non-parametric VMD, empirical mode decomposition, total least-squares estimation of signal parameters via rotational invariance techniques, and Prony on the performance of mode parameter identification. Results show that the IVMD method effectively overcomes the shortcomings of those methods mentioned above in dealing with mode mixing, noise sequence, and non-stationary signals. Finally, the feasibility of the proposed method in extracting the low-frequency oscillation mode parameters of power system is verified by the simulation signals of the IEEE two-area four-generator power system and the New England 39-bus system.

GMAT: Glottal closure instants detection based on the Multiresolution Absolute Teager–Kaiser energy operator

Glottal Closure Instants (GCIs) detection is important to many speech applications. However, most existing algorithms cannot achieve computational efficiency and accuracy simultaneously. In this paper, we present the Glottal closure instants detection based on the Multiresolution Absolute TKEO (GMAT) that can detect GCIs with high accuracy and low computational cost. Considering the nonlinearity in speech production, the Teager–Kaiser Energy Operator (TKEO) is utilized to detect GCIs and an instant with a high absolute TKEO value often indicates a GCI. To enhance robustness, three multiscale pooling techniques, which are max pooling, multiscale product, and mean pooling, are applied to fuse absolute TKEOs of several scales. Finally, GCIs are detected based on the fused results. In the performance evaluation, GMAT is compared with three state-of-the-art methods, MSM (Most Singular Manifold-based approach), ZFR (Zero Frequency Resonator-based method), and SEDREAMS (Speech Event Detection using the Residual Excitation And a Mean-based Signal). On clean speech, experiments show that GMAT can attain higher identification rate and accuracy than MSM. Comparing with ZFR and SEDREAMS, GMAT gives almost the same reliability and higher accuracy. In addition, on noisy speech, GMAT demonstrates the highest robustness for most SNR levels. Additional comparison shows that GMAT is less sensitive to the choice of scale in multiscale processing and it has low computational cost. Finally, pathological speech identification, which is a concrete application of GCIs, is included to show the efficacy of GMAT in practice. Through this paper, we investigate the potential of TKEO for GCI detection and the proposed algorithm GMAT can detect GCIs with high accuracy and low computational cost. Due to the superiority of GMAT, it will be a promising choice for GCI detection, particularly in real-time scenarios. Hence, this work may contribute to systems relying on GCIs, where both accuracy and computational cost are crucial.

Crack Identification in CFRP Laminated Beams Using Multi-Resolution Modal Teager-Kaiser Energy under Noisy Environments.

Carbon fiber reinforced polymer laminates are increasingly used in the aerospace and civil engineering fields. Identifying cracks in carbon fiber reinforced polymer laminated beam components is of considerable significance for ensuring the integrity and safety of the whole structures. With the development of high-resolution measurement technologies, mode-shape-based crack identification in such laminated beam components has become an active research focus. Despite its sensitivity to cracks, however, this method is susceptible to noise. To address this deficiency, this study proposes a new concept of multi-resolution modal Teager–Kaiser energy, which is the Teager–Kaiser energy of a mode shape represented in multi-resolution, for identifying cracks in carbon fiber reinforced polymer laminated beams. The efficacy of this concept is analytically demonstrated by identifying cracks in Timoshenko beams with general boundary conditions; and its applicability is validated by diagnosing cracks in a carbon fiber reinforced polymer laminated beam, whose mode shapes are precisely acquired via non-contact measurement using a scanning laser vibrometer. The analytical and experimental results show that multi-resolution modal Teager–Kaiser energy is capable of designating the presence and location of cracks in these beams under noisy environments. This proposed method holds promise for developing crack identification systems for carbon fiber reinforced polymer laminates.