Vold-Kalman Filter Research Articles

Induction Motor Tacholess Fault Detection in Transient Speeds Using Adaptive Generalized Vold Kalman Filter

Fault detection are essential in machine condition monitoring to ensure reliable and efficient operations. This article introduces a methodology to achieve this goal, using tacholess method. Techniques such as the Hilbert transform, adaptive observer, generalized demodulation transform (GDT), and Vold-Kalman filtering (VKF) are combined. The novelty introduced in this article lies in the use of the adaptive observer and the incorporation of the estimated speed to make the generalized Vold-Kalman filter adaptive as a function of motor current. Experimental evaluations were carried out, simulating artificial defect, corresponds to a scenario where the rotor has multiple impacts per revolution, often associated with issues such as misalignment or imbalance. These experimental findings demonstrate the performance of the proposed method, with an adaptive filter showing improved signal extraction across a range of operating situations. A diagnostic protocol has been developed, using statistical analysis, to guarantee the applicability of the method under all operating conditions.

A novel generalized Vold-Kalman filtering for wind turbine fault diagnosis

Fault diagnosis of offshore wind turbines (WTs) is vital to the reliability and efficiency of wind power generation. Generalized demodulation has been demonstrated to be effective in revealing the fault-related frequencies, but there are intricate interfering components in the demodulation spectra due to the iterative demodulation operation and the complex modulation nature of vibration signals of WT. This paper develops a novel generalized Vold-Kalman filtering approach. To separate the signal components, Vold-Kalman filter is adopted to the amplitude envelope of vibration signal by exploiting its merit in non-component decomposition, in which a frequency set is constructed by the modulation nature of machinery vibration. The phase functions of the frequencies in the frequency set are constructed, by which the variable components are transformed into constant ones. The proposed method is tested via the data of rolling bearings and a WT planetary gearbox.

Bearings fault diagnosis under variable speed conditions by hypothesis-based FRFT technique

The vibration signals of faulty bearings under non-stationary conditions are inherently multi-component and time-varying, which presents a challenge for effective fault diagnosis. Considering the vibration characteristics of rolling bearings under non-stationary conditions and taking advantage of the Fractional Fourier Transform (FRFT), a novel diagnosis method based on the hypothesis-based FRFT has been proposed to separate the fault components. First, the fault characteristic frequencies (FCFs) are extracted from the time-frequency representation of the vibration signals, and the Vold-Kalman filtering is employed to eliminate the influence of noises and other interference components. Subsequently, the fractional feature model is constructed to obtain speed information by the hypothesis approach, whose central idea is that the rotational frequency (RF)-related frequencies under different fault types are estimated, based on the extracted FCFs and the fault characteristic orders. Finally, fault diagnosis is completed by the RF-related peaks in the final spectrum. The method eliminates the need for rotational speed measurement devices and angular resampling. Simulation and experiment estimation results show that the hypothesis-based FRFT method can accurately locate fault characteristic components of bearings under non-stationary conditions.

Multicomponent collaborative time-frequency state-space model for vibration signal decomposition under nonstationary conditions

The implementation of prognostics and health management strategies is essential for enhancing the safety and maintenance of rotating equipment in chemical plants. The examination of vibration signal behaviours under variable-speed conditions and the development of signal decomposition methods in such contexts are of substantial theoretical and practical relevance. This paper proposes a novel multicomponent collaborative time-frequency state-space method for the decomposition of vibration signals. The method employs a multi-component proportional model to accurately describe the synchronisation of high-frequency components with the rotational frequency component. Based on this framework, the instantaneous frequency change curves of multiple components are input into the Vold–Kalman filter algorithm for precise decomposition of multicomponent vibration signals under variable-speed conditions. Experimental results demonstrate the effectiveness of the proposed method in achieving accurate instantaneous frequency tracking and signal decomposition, showing clear advantages over traditional methods.

Single-tone Aerodynamic Noise Source Separation for Gas Turbines

The aerodynamic noise in the gas turbines primarily originates from the pulsations generated by the air within compressors, and it is a combination of single-tone noise caused by the pressure fluctuation of blades and broadband noise generated by interactions between turbulent fluid and blades. Therefore, the separation of single-tone noise is vital in predicting the contribution of each noise source for noise reduction and health monitoring. In current practice, the Vold-Kalman filter (VKF) is widely employed for single-tone noise separation. However, the optimal VKF bandwidth is often difficult to determine, thereby impeding the separation accuracy of single-tone noise. To solve this problem, this paper proposes a single-tone noise separation method by utilizing computed order tracking based on double criteria VKF (DC-VKF). Firstly, the order spectrum of the original signal is obtained by order analysis. Secondly, the relative error of order amplitude (REOA) and total relative standard deviation (TRSD) of the extracted signal are calculated under different bandwidths and corresponding curves are separately carried out. The optimal bandwidth is determined by identifying the first bandwidth that meets either the REOA or TRSD threshold, which are respectively set based on trend of curves. Finally, the corresponding order components are separated by VKF with optimized bandwidth. The effectiveness of DC-VKF is validated on simulation and gas turbine datasets. This paper provides an efficient extraction method for the separation of single-tone aerodynamic noise of gas turbines, and provides a scientific basis for noise monitoring, evaluation, and reduction.

Acoustic measurements of full-scale electric vertical takeoff and landing aircraft

The Advanced Air Mobility industry is progressing rapidly towards the goal of revolutionizing transportation by connecting urban and underserved communities with electric vertical takeoff and landing (eVTOL) aircraft. To achieve widespread use, eVTOL aircraft must generate acceptable noise in surrounding communities. Many eVTOL aircraft currently under development have novel configurations of rotors, propellers, and wings that may produce rotor-rotor and rotor-airframe interaction noise at certain flight conditions. Acoustic measurements of full-scale eVTOL aircraft are critical to understand the complex noise-generation mechanisms and to validate aeroacoustic models for these novel aircraft designs. In this presentation, we present acoustic measurements of Hexa, an 18-rotor, single-passenger eVTOL aircraft developed by LIFT Aircraft, Inc. We apply acoustic source characterization techniques using simultaneous acoustic measurements and vehicle telemetry data to provide a better understanding of the noise-generation mechanisms. One such analysis technique is the Vold-Kalman filter, which we apply to auralize the tonal waveforms of individual rotors. Finally, we discuss plans for upcoming acoustic measurements of a full-scale, multi-passenger eVTOL aircraft. These measurements and analyses provide the data and tools required to better understand the noise-generation mechanisms and to validate aeroacoustic models for full-scale eVTOL aircraft

Improved multi-order Vold-Kalman filter for order tracking analysis using split cosine and sine terms

Order tracking analysis is an effective tool for the analysis of non-stationary vibration and acoustical signals for the purposes of machinery fault diagnosis and operational modal analysis. The second-generation Vold-Kalman filter is widely used for order tracking analysis; however, the formulation of the data equation is based on incomplete complex kernels, which introduce an imaginary part error in the cost function. In this work, the data equation of the second generation Vold-Kalman filter is re-formulated using separated cosine and sine kernels that necessarily provide a real-valued sum. Doing so will minimize the error in the data equation and offer better optimization scheme to reduce the error in the structural equation and; hence, provide smooth envelopes. Unlike Vold-Kalman method which requires high filter weighting factors to suppress envelope artifacts, the proposed method can achieve high accuracy even when using small weighting factor as deduced from the simulation and experimental investigations. The proposed method can be used to measure the envelopes of close and crossing orders, as well as orders experiencing resonance conditions or orders with high slew rate due to lower filter decay time.

Vold–Kalman filter order tracking of axle box accelerations for track stiffness assessment

Intelligent data-driven monitoring procedures hold enormous potential for ensuring safe operation and optimal management of railway infrastructure in the face of increasing demands on cost and operations efficiency. Numerous studies have highlighted track stiffness as a main parameter influencing the evolution of degradation that drives maintenance processes. As such, the measurement of track stiffness is fundamental for characterizing the performance of the track in terms of deterioration rate and noise emission. In this work, we propose a rail stiffness assessment scheme relying on low-cost, on board monitoring sensors, namely axle-box accelerometers, that are mounted on in-service trains and enable frequent, real-time monitoring of the railway infrastructure network. A Vold–Kalman filter is proposed for decomposing the signal into periodic wheel and track related excitation–response pair functions. We demonstrate that these components are in turn correlated to operational conditions, such as wheel out-of-roundness and the rail type. We further illustrate the relationship between the track stiffness, the measured wheel-rail forces and the sleeper passage amplitude, which can ultimately serve as an indicator for predictive track maintenance and prediction of track durability.

The space-time structure of sound produced by stacked rotors in hover using Vold-Kalman filters and proper orthogonal decomposition

Proper orthogonal decomposition and the Vold-Kalman order tracking filter are combined to evaluate the most energetic components of the sound field produced by a coaxial, co-rotating rotor in hover. The study leverages the database generated by Tinney and Valdez (2020; AIAA J. vol. 58, no. 4) comprising an array of eight stationary microphones oriented to capture the acoustic near-field below the rotor disk plane where ground observers are expected to reside and where concerns over community annoyance are greatest. Changes to rotor conditions focus primarily on rotor speed and index angle (angular separation between the upper and lower rotors), as this has the greatest effect on the sound field produced by stacked rotors by way of the constructive and destructive interference of the sound generated, separately, by the upper and lower rotors. Proper orthogonal decomposition is performed using a kernel constructed from auto and cross-spectral densities of the spatially coherent sound field. The eigenvectors demonstrate the spatial extent of the sound field for discrete frequencies corresponding to the first few blade pass frequency harmonics. In order to improve the clarity and accuracy of the low-order reconstructions, a second generation, Vold-Kalman multi-order tracking filter is employed to isolate discrete frequencies. Relative to conventional spectral filtering methods, the Vold-Kalman filter is performed in the time-domain and is shown to accurately isolate discrete tones while preserving changes to the phase of the signal. Findings from this analysis reveal the effect of index angle on the spatial make-up of the coherent sound field produced by hovering stacked rotors.

Online detection of interturn short-circuit fault in induction motor based on 5th harmonic current tracking using Vold-Kalman filter

<span lang="EN-US">In this paper we propose a strategy for real-time detection of interturn short-circuit faults (ISCF) on three-phase induction motor (IM) by using a Vold-Kalman filter (VKF) algorithm. ISCF produce a thermal stress into the stator winding due to large current that flows through the short-circuited turns. Therefore, incipient fault detection is required in order to avoid catastrophic failures such as phase to phase, or phase to ground faults. The strategy is based on an analytical IM model that includes a ISCF fault in any of the phase windings and considering the </span><em><span lang="EN-US">h<sup>-th</sup></span></em><span lang="EN-US"> harmonic in the voltage supply. Based on equivalent electrical circuits with harmonics in sequence components, we propose a strategy for detection of an ISCF on IM by tracking the 5<sup>th</sup> harmonic current component using a VKF algorithm. The proposed model is experimentally validated using a three-phase IM with modified stator windings to generate ISCF. Also, the IM is feeded by a programmable voltage source to synthesize distorted voltage supply with the 5<sup>th</sup> harmonic. The results demonstrated that the positive-sequence magnitude for the 5<sup>th</sup> harmonic current component is a good indicator of the fault severity once it exceeds a threshold limit value, even under load variations and unbalanced voltages.</span>

An enhanced instantaneous angular speed estimation method by multi-harmonic time–frequency realignment for wind turbine gearbox fault diagnosis

Gearboxes are one of the most critical transmission devices in wind turbines (WTs). Order tracking (OT) of variable-speed WT gear is a powerful means to carry out fault diagnosis. Since it is difficult to install a tachometer or encoder for gearboxes with limited structural space, it is impossible to obtain the instantaneous angular speed (IAS) of the gearbox. In recent years, many tacholess techniques have been presented to estimate instantaneous phase from vibration signals for OT. However, their performance needs to be further improved to get a more exact diagnosis result. To solve this issue, this paper presents an enhanced IAS estimation approach for WT tacholess order tracking (TLOT), which is available for accurate IAS estimation of the rotating shaft, so that TLOT can be more effectively conducted under conditions of large speed variation and background noise. An improved cost function algorithm is designed to extract the IAS from the vibration signal. A Vold–Kalman filter and Hilbert transform are combined to calculate the instantaneous phase. Afterwards, the raw non-stationary vibration signal is resampled at an equal angle increment, and the envelope order spectrum is calculated from the resampled signal for fault diagnosis of the WT gearbox. The main innovating idea of this approach is to improve the traditional cost function ridge-extraction method by introducing gradient information based on probability and multi-harmonic time–frequency realignment, which makes the IAS estimation process more accurate and overcomes the limitations of traditional IAS estimation techniques. The effectiveness of the presented approach is demonstrated by using a vibration signal measured from real-world WT gearboxes, and the validation results demonstrate that the presented approach surpasses some state-of-the-art methods in IAS estimation accuracy and efficiency.

Gas turbine blade fracturing fault diagnosis based on broadband casing vibration

Blade fault is a catastrophic failure of gas turbines. In order to improve the reliability of blade during operation, condition monitoring is one of the effective methods. However, there always exist two problems with blade monitoring: 1) challenges in warning of the occurrence of blade failure in advance and 2) difficulties finding the location after blade failure. In this article, we solve these problems by excavating the characteristics of blade-related signals in broadband casing vibration with advanced signal processing methods and machine learning technology. First, a novel method--Sparse Harmonic Product Spectrum (SHPS)--is proposed to accurately calculate blade passing frequency from gas turbine broadband casing vibration. The SPHS relies on Fourier transform, and its calculation utilizes the physical relationship between fundamental frequency and blade passing frequencies. Combining Vold-Kalman filter with adaptive parameter optimization process (AVKF), the blade-related vibration can be separated from casing vibration even in strong noise. Analysis of simulated casing vibration signal is used to verify the effectiveness and superiority of proposed method. Based on blade-related vibration, we build a gas turbine blade condition model in an unsupervised learning manner. The model can excavate potential blade failures earlier and more accurately than conventional threshold methods. Then, three coefficients are constructed according to the blade-related vibration characteristics to identify the blade fault location in multi-stage system. Moreover, the effectiveness of the proposed blade diagnosis framework is verified using actual industrial gas turbine blade fracturing failure data.

Identification and separation of coupled vibration sources in multi-rotor gas turbines under time-varying speed conditions

Vibration sources in multi-rotor gas turbines under time-varying speed conditions are strongly coupled in the time–frequency domain, which prevents further mining of dynamic information from measured signals. Hence, a novel scheme of vibration source identification and separation is proposed to obtain individual source information. Firstly, the order and resonance components are identified by order analysis, and precise order numbers are further determined by computed order tracking. Then, in four typical vibration source coupling scenarios, the performances of Vold-Kalman filter (VKF), several typical adaptive mode decomposition methods and derivative methods are comparatively studied using Jeffcott rotor simulation system. Finally, the optimal source separation based on VKF and variational mode decomposition/extraction (VMD/VME) is determined. Furthermore, the settings of VKF filter bandwidth are studied quantitatively, and the effects of VMD and VME penalty factors are analyzed. In conclusion, the proposed scheme effectively identifies and accurately separates vibration sources from the test bed and gas turbine datasets, which provides important evidences for vibration monitoring and control as well as vibration transmission analysis of gas turbines.

Feature extraction by enhanced time–frequency analysis method based on Vold-Kalman filter

The time–frequency analysis method can extend a one-dimensional signal to a two-dimensional time–frequency plane, revealing the signal's time-varying characteristics. The time–frequency representation (TFR) obtained by the time–frequency postprocessing algorithm has the characteristics of energy aggregation and high resolution. The generalized S-synchroextracting transform (GS-SET) stands out for its strong adaptability. However, this method cannot obtain effective information when analyzing multicomponent complex signals. We propose an enhanced time–frequency analysis method to solve this problem. First, the multicomponent complex signal is decomposed into multiple mono-component signals by the Vold-Kalman time-varying filtering technique. Second, these signals are processed by the GS-SET method. Last, the obtained TFRs are linearly superimposed to obtain the results of the enhanced method. The simulated signal verifies that the proposed method can effectively represent its time-varying characteristics. The experimental signal of the rolling bearing verifies the practicability of this method.

A novel order spectrum-based Vold-Kalman filter bandwidth selection scheme for fault diagnosis of gearbox in offshore wind turbines

Vold-Kalman order tracking filter is an effective technique for dealing with non-stationary vibrations which offshore wind turbines often encounter. It has a unique capability to extract and track the time waveforms of harmonics in short transients without phase bias, and this capability is beneficial to the condition monitoring of offshore wind turbines. In general, the accuracy of the tracking results of the Vold-Kalman filer for condition monitoring is heavily dependent on the selection of filter bandwidth. A fixed filter bandwidth becomes problematic when processing different types of signals under varying operating conditions. Significant errors may arise in the tracking, rendering the condition monitoring of offshore wind turbines unreliable. To address this issue, this paper proposes a novel scheme for Vold-Kalman filter bandwidth selection to guarantee the consistency and accuracy of the offshore wind turbine condition monitoring process, ensuring reliable fault diagnosis. A numerical model is used to evaluate the effectiveness of the proposed bandwidth selection scheme first. Then the proposed scheme is further validated through the offshore wind turbine planetary gearbox datasets, together with the demonstration of the fault diagnosis capability of the filtered results.

Synchro-Reassigning Scaling Chirplet Transform for Planetary Gearbox Fault Diagnosis

It is difficult for classic time-frequency analysis (TFA) methods to characterize close-spaced nonlinear frequency curves with satisfactory time-frequency concentration and adaptively decompose above frequency components. As such, a novel TFA technique, termed synchro-reassigning scaling Chirplet transform (SRSCT) is developed in this paper. The proposed SRSCT is inspired by the scaling-basis Chirplet transform (SBCT) and reassignment theory. The novelties of the SRSCT are concluded as (a) a synchro-reassigning operator (SRO) is constructed for adaptively calculating the ideal time-frequency amplitudes on the instantaneous frequency (IF) ridges from the SBCT result and removing other smeared time-frequency coefficients, as a result, time-frequency resolution of the novel time-frequency representation (TFR) is greatly improved, close-spaced frequency curves are clearly characterized and noise interference is eliminated; and (b) perfect adaptive mode decomposition ability is achieved by combining the SRO, ridge detection method and vold-Kalman filter (VKF). Analysis results of the simulated signal show the effectiveness of the proposed SRSCT. Experimental analysis on faulty planetary gearbox signal shows that the proposed method can clearly characterize fault features. Compared with eight classic TFA methods, the Rényi entropies of the TFRs calculated by the proposed method are smallest in two cases, and they are 2.75 and 3.03, respectively, which means that the SRSCT can generate the TFR with the highest energy concentration.

A novel adaptive bandwidth selection method for Vold–Kalman filtering and its application in wind turbine planetary gearbox diagnostics

The planetary gearbox transmission system in wind turbines has complex structures and generally operates under non-stationary conditions. Thus its measured responses are of high complexity and nonlinearity, which brings a great challenge in the development of reliable condition monitoring techniques for the planetary gearbox transmission system. As a prevalent and effective tool for analyzing the non-stationary vibration signal with strong nonlinearity, the Vold–Kalman filtration technique has excellent capabilities of tracking the targeted harmonic components of vibrations, which can significantly benefit planetary gearbox fault diagnostics. However, the tracking accuracy is heavily enslaved to the selection of the rational bandwidth for the Vold–Kalman filter. An inappropriate bandwidth could impair the characteristics of the targeted harmonic responses, and as a consequence, the monitoring process becomes no longer reliable. To address this issue, a novel bandwidth selection methodology for the Vold–Kalman filter is developed in this paper. Through comprehensively depicting the targeted harmonic response using features in multiple domains, the rational bandwidth can be selected for Vold–Kalman filtering, and then, a reliable monitoring process can be ensured. Additionally, a tacho-less speed estimation procedure is utilized in this paper to acquire the instantaneous rotational speed from the vibration signal directly. With the rational bandwidth and the estimated rotational speed, the desired harmonic components of vibrations can be adaptively extracted and tracked through the Vold–Kalman filter with high accuracy, and at the same time, the irrelevant or unwanted components are excluded completely. The effectiveness and superiority of the proposed adaptive Vold–Kalman filtration for wind turbine planetary gearbox diagnostics are demonstrated and validated experimentally.

Aerodynamic noise separation of helicopter main and tail rotors using a cascade filter with Vold-Kalman filter and cyclic Wiener filter

The noise issue has become an important factor limiting the massive application of helicopters as the requirements for helicopter reliability and comfort continue to increase. As the primary noise source of helicopters, the main and tail rotor aerodynamic noise should be separated for individual noise reduction investigations. According to the frequency domain characteristics, the rotor aerodynamic noise can be divided into tonal noise and broadband noise. A cascade filtering method with Vold-Kalman filter and cyclic Wiener filter is proposed in this paper to separate the tonal and modulated broadband noise of the main and tail rotors, respectively. The classical method only considers the periodic characteristics of the main and tail rotor aerodynamic noise for harmonic separation. The broadband noise is not considered within the separation of interest due to its randomness, which leads to the inaccuracy of the conventional method for the aerodynamic noise separation of the main and tail rotors. The broadband noise exhibits a second-order cyclostationarity due to the periodic modulation of the rotational motion of the rotor. According to its cyclostationarity, while considering the periodicity of tonal noise for harmonic separation, the proposed cascade filtering method also performs the separation of broadband noise. More precise separations of the main and tail rotor can be obtained by this method. The efficacy of the proposed cascade filtering method is demonstrated in both the simulation and wind tunnel noise measurement.

Noise source localization in permanent magnet synchronous motors under time-varying speed working conditions

Noise source localization of rotating machinery plays an important role in machinery noise diagnosis and control. Various beamforming methods have been developed for stationary sound source localization. However, for rotating machinery working under time-varying speed conditions, the radiated acoustic signals are typically nonstationary. Under these conditions, characterizing and localizing nonstationary sound sources remains a challenge. Permanent magnet synchronous motors are one of the most widely used rotating machinery in modern industries and often work under variable speed conditions. Herein, the noise source localization problem of motors under time-varying speed conditions was studied. A nonstationary noise source localization method based on the Vold-Kalman filter and time-domain beamforming is proposed to restore the spatial acoustic maps of permanent magnet synchronous motors(PMSMs) at a characteristic order. First, the Vold-Kalman filter is adopted to extract acoustic signals at a characteristic order from the nonstationary measurements using a microphone array. Then, the filtered multichannel acoustic signals are fed into the time-domain beamforming algorithm to obtain the noise source localization result in a characteristic order. Combining Vold-Kalman filter with time-domain beamforming enables the characterization of non-stationary sound sources in the time, spatial, and order domains. The experimental results verify the effectiveness of the proposed method in noise source localization for motors under time-varying speed conditions. In addition, the experimental case with two motors further proves that the proposed method can simultaneously realize noise source separation at different characteristic orders.

Mechanical faults detection for vehicle motors under nonstationary conditions based on Vold-Kalman order tracking method

The fault diagnosis and health management of motors are the key technology that needs to be resolved in the future with the development of electric vehicles. The drive motors usually working under nonstationary conditions. Moreover, the mechanical fault is the most common type among the motor fault types. Therefore, developing the mechanical fault detection method under variable speed conditions would be of great value to improve the diagnosis accuracy of vehicle motors. This paper deals with the mechanism of the bearing fault, the rotor eccentricity fault, and their compound fault of permanent magnet synchronous motors. The purpose of this paper is to propose a mechanical fault detection method based on Vold-Kalman for vehicle motors under variable working conditions. First, the vibration characteristics of the healthy and the faulty motors are analyzed. Next, for eliminating the influence of variable conditions on the mechanical-fault detection, the fault characteristics are extracted by applying the Vold-Kalman filter. Finally, experiments are carried out based on the selected part of the new European driving cycle test conditions. The experimental results show that the proposed approach can detect the mechanical fault of the motor under nonstationary conditions effectively.