Periodic Impulses Research Articles

A novel fault diagnosis method for bearing based on maximum average kurtosis morphological deconvolution

Abstract Maximum average kurtosis deconvolution (MAKD) effectively enhances periodic impulses in vibration signals. However, under conditions of random impulse interference, MAKD tends to amplify impulses within a single period. To address this problem, this paper proposes a maximum average kurtosis morphological deconvolution (MAKMD) method. First, on the basis of proposing a time-varying structural element more in line with the characteristics of vibration signals and constructing a new morphological gradient squared operator, an enhanced time varying morphological filtering (ETVMF) is proposed. Then, ETVMF is introduced into MAKD to eliminate the effect of random impulse. Finally, the diagonal slice spectrum (DSS) is utilized to detect the coupling frequency of the bearing, which makes the spectrum clearer and more convenient for bearing fault diagnosis. In MAKMD, the effect of random impulse is eliminated and the capability of fault feature extraction is enhanced. To demonstrate the method’s effectiveness and feasibility, experiments are conducted using simulated signals and measured bearing fault data, comparing results with existing deconvolution methods.

Double autocorrelation-based cyclicity evaluation for repetitive transients feature extraction

Abstract The vibration response caused by bearing local defects has impact and periodicity in waveform, which provides a standard for the frequency band selection in envelope analysis. However, most periodicity measurements without prior knowledge belong to sparsity evaluation, while the defects of sparsity index in nature are inevitable. Inspired by the periodic component extraction of autocorrelation function, a novel cyclicity measurement based on double autocorrelation calculation is proposed. With the help of normalization, this approach can distinguish periodic impulses from random impulses by using the periodic sub-maxima of the envelope autocorrelation. Considering the influence of the noise component on the autocorrelation of the periodic signal, the sub-maximums are maintained by threshold processing. On this basis, the re-autocorrelation is calculated to identify the periodic sub-maximum. Finally, as a non-prior index, a demodulation band selection is also proposed in combination with an impulsivity evaluation. The results of the proposed method are analyzed and verified by comparison with typical methods.

HTG transformation: an amplitude modulation method and its application in bearing fault diagnosis

Abstract Rolling bearings are critical components in modern mechanical equipment, and the health monitoring and predictive maintenance of bearings are crucial for the normal operation of machinery. Hence, there is a compelling need to delve into advanced methodologies for enhancing the detection of fault characteristics in bearings. Faulty bearings produce periodic impulses during constant-speed rotation, which can typically be detected through envelope analysis. However, in some complex conditions, the relevant fault frequencies may be hidden within interfering components. This paper presents an amplitude modulation technique called the hyperbolic tangent Gaussian (HTG) transformation, designed to extract weak fault components from signals. Firstly, a family of amplitude modulation functions, known as the HTG functions, is constructed. These functions modulate signals with normalized amplitudes to obtain a series of modulated signals. Simultaneously, a frequency domain amplitude ratio metric is used for the automatic selection of the optimal components. Finally, the HTGgram is introduced, a spectral decomposition method based on trend components, aiming to identify the best combination of filtering and modulation components. Simulations with multi-component bearing fault signals and experimental signals with composite bearing faults demonstrate that this method not only highlights fault features and suppresses noise interference but also adaptively selects frequency bands related to faults, enhancing fault information. This approach exhibits excellent adaptability and effectiveness in complex operating conditions with multiple interference components.

Multi-rolling element faults diagnosis of rolling bearing based on time-frequency analysis and multi-curves extraction

Abstract In industrial production, rolling bearings are widely used as key mechanical components in all types of rotating machinery. Fault diagnosis is essential for predicting bearing damage in advance, avoiding sudden equipment downtime and reducing economic losses. However, rolling element fault diagnosis of rolling bearings continues to be a challenge, especially with multi-rolling element faults. In view of the characteristics of randomness, weakness, and coupling in the vibration signal generated by multi-rolling element faults in rolling bearings, a multi-rolling element fault detection method is proposed by combination time-frequency (TF) analysis (TFA) with multi-curves extraction methods. The pre-processing method combined autoregressive model with maximum correlated kurtosis deconvolution is employed to enhance the weak periodic fault impulses in the raw vibration signals of the rolling bearing. Then an improved dynamic path multi-curves extraction method is proposed to extract multiple TF curves from the TF spectrogram (TFS) constructed via short-time Fourier transform. According to the proposed classification criteria, the TF curves are classified as homologous faults. The TF masking (TFM) method is employed to keep TF information closely associated with the fault impulse. Finally, the fault signals are reconstructed sequentially based on the TFS processed by TFM, and precise identification of multi-rolling element faults is achieved by envelope analysis. Experimental results demonstrate the effectiveness of the proposed method in extracting the weak fault features of multi-rolling elements and accomplishing fault separation and diagnosis.

Optimal Control of Harvesting of a Distributed Renewable Resource on the Earth’s Surface

This paper is devoted to the optimal control of mixed (stationary and periodic impulse) harvesting of a renewable resource distributed on the Earth’s surface. Examples of such a resource are biological populations, including viruses, chemical contaminants, dust particles, and the like. It is proved that on an infinite planning horizon, there exists an admissible control ensuring the maximum of time-averaged harvesting.

Objective sound quality evaluation of the electric two-stage centrifugal compressor for fuel cell vehicles-experimental investigations

Sound quality is one of the most challenging studies in the field of automotive NVH. The most important noise source in fuel cell vehicles (FCVs) is the air compressor, and its noise seriously affects the sound quality of FCVs. The centrifugal compressor is now the mainstream choice for commercial FCVs, but there are few studies on its sound quality evaluation using objective psychoacoustic parameters. Therefore, a comprehensive vibration-noise experiment is conducted on an electric two-stage centrifugal compressor (ETCC) for FCVs to evaluate the sound quality accurately, including all operating conditions. The sound quality is evaluated by four objective psychoacoustic parameters: loudness, sharpness, fluctuation strength and roughness, which are the most widely used indicators. The reasons for the variation of these acoustic parameters under dynamic operating conditions are accordingly explained. It can be concluded that the loudness and sharpness show a strong and positive correlation with the rotational speed, while the fluctuation strength and roughness just reflect the sound quality of the ETCC for the low-frequency band and high-frequency band, respectively. So, taking loudness and sharpness as the core indicators under accelerating conditions is recommended. Then, the sound quality of the ETCC under unstable conditions at variable speeds is investigated. It is found that the sound quality of the ETCC deteriorates under surge conditions. When entering into the deep surge, the loudness and sharpness both fluctuate drastically, which is caused by the periodic impulse noise. The fluctuation strength rises sharply and keeps a high level in the process of deep surge because of the obvious low-frequency characteristics of the surge. The above three parameters have a clear correlation with the rotational speed, while roughness is the only parameter that is not significantly connected with the rotational speed, which can be explained by the existence of a high-frequency fluctuation under the entire surge process. Finally, the causes of sound quality deterioration are explored using secondary signal processing. The results show that the outlet pressure pulsations of the ETCC under surge conditions lead to the increases and fluctuations of these acoustic parameters, and compressor surge is the main cause of deterioration in sound quality for FCVs. Based on the results, the objective sound quality evaluation of the ETCC is accomplished, and four psychoacoustic parameters can be modified to improve the sound quality. This study provides a theoretical basis for proposing methods to accurately evaluate and improve the sound quality of FCVs.

Sliding time synchronous averaging based on independent extended autocorrelation function for feature extraction of bearing fault

Extracting fault feature is a key challenge during the early failure stage of bearings due to weak fault components and strong background noises. To solve this problem, an extension operation is introduced, and a novel algorithm called independent extended autocorrelation function is proposed. Subsequently, based on time synchronous averaging, the sliding time synchronous averaging method is developed to further enhance periodic components. The time dimension is added to generate a series of periodic impulses, which is advantageous to directly extract the fault characteristic. Therefore, the presented algorithm is called the sliding time synchronous averaging based on independent autocorrelation function (STSA-IEACF). Numerically simulated signals and two experimental datasets are employed to compare the performance of the STSA-IEACF with the mainstream blind deconvolution methods in fault feature extraction of bearing. The results show that the proposed algorithm performs better than the others in this terms of extracting fault characteristics.

Asymptotic Behavior of <i>n</i>th Order Impulsive Differential Equations

This paper devotes to the asymptotic behavior of all solutions of nth order impulsive differential equations. Based on impulsive differential inequality, boundedness and zero tendency of every solution for nth order impulsive differential equations are obtained. In addition, we derive globally uniformly exponential stability of every solution under Lyapunov function and impulsivetechnique, and these results are extend to <i>n</i>th order differential equations with periodic coefficient and periodic impulse. Meanwhile, an example with simulations are provided to verify the conclusion.

A periodic-modulation-oriented noise resistant correlation method for industrial fault diagnostics of rotating machinery under the circumstances of limited system signal availability

The periodical impulses caused by localized defects of components are the vital characteristic information for fault detection and diagnosis of rotating machines. In recent years, multitudinous spectrum analysis-based signal processing methods have been developed and authenticated as the powerful tools for excavating fault-related repetitive transients from the measured complex signals. Nonetheless, in practice, their applications can be severely confined by the constraints of limited system signal availability and incomplete information extraction under intricate noise interferences. To tackle the aforementioned issues, this paper proposes a periodic-modulation-oriented noise resistant correlation (PMONRC) method for target period detection and fault diagnosis of rotating machinery. Firstly, the envelope of raw signal is obtained via a novel sequential procedure of signal element-wise squaring, spectral Gini index-guided adaptive low-pass filtering, and signal element-wise square root computation, to highlight the modulated wave component that is more likely to be related to the potential fault-induced periods. Subsequently, a series of sub-signals, which can encode the fault-related repetitive information and enhance noise resistance, are constructed utilizing the envelope signal. Based upon the envelope signal and the obtained sub-signals, a weighted envelope noise resistant correlation function can be derived with the assistance of the L-moment ratio-based indicator and Sigmoid transformation. Finally, the specific fault type of the rotating machinery can be identified and affirmed accordingly. The proposed PMONRC method, which is nonparametric and completely adaptive to the signal being processed itself, overcomes the deficiencies of spectral analysis-based approaches, and is applicable for the engineering circumstances of system signal limitation and low signal-to-noise ratio (SNR), possessing immense practical merit. Both simulation analyses and experimental validations profoundly demonstrate that the proposed method is superior to other existing state-of-the-art time-domain correlation methods. Moreover, as an attempt as well as exemplar to apply this method, the PMONRC-based incipient fault diagnostic results of rolling bearing data from the well-known experimental platform PRONOSTIA are presented and discussed as well, to further elucidate the effectiveness and practical engineering significance of the proposed method.

Modeling the Electrical Activity of the Heart via Transfer Functions and Genetic Algorithms.

Although healthcare and medical technology have advanced significantly over the past few decades, heart disease continues to be a major cause of mortality globally. Electrocardiography (ECG) is one of the most widely used tools for the detection of heart diseases. This study presents a mathematical model based on transfer functions that allows for the exploration and optimization of heart dynamics in Laplace space using a genetic algorithm (GA). The transfer function parameters were fine-tuned using the GA, with clinical ECG records serving as reference signals. The proposed model, which is based on polynomials and delays, approximates a real ECG with a root-mean-square error of 4.7% and an R2 value of 0.72. The model achieves the periodic nature of an ECG signal by using a single periodic impulse input. Its simplicity makes it possible to adjust waveform parameters with a predetermined understanding of their effects, which can be used to generate both arrhythmic patterns and healthy signals. This is a notable advantage over other models that are burdened by a large number of differential equations and many parameters.

An improved envelope spectrum via Hoyer index-gram for bearing fault extraction

Resonance demodulation is one of the most commonly used methods in rolling bearing fault diagnosis, yet determining the optimal demodulation band has been a significant challenge. The vibration signal from a faulty bearing may include not only periodic fault impulses but also discrete harmonic interferences, random impulses, Gaussian white noise, among others. To enhance fault information and attenuate the impact of interference signals, this paper proposes an improved envelope spectrum via Hoyer index-gram (IESHoyergram). By utilizing the Hoyer index of the spectrum-related enhanced envelope spectrum as the frequency band filtering criterion, the proposed method extracts periodic impulses while suppressing interference from random impulses and other sources. Moreover, owing to the multilevel segmentation based on the different trend components in the spectral correlation spectrogram, IESHoyergram avoids the shortcomings of traditional segmentation methods. The proposed method is validated through both simulated and experimentally acquired data, demonstrating its capability not only to enhance the characteristics of a single fault but also to separate multiple component faults.

Distributed sliding mode control for a class of impulsive uncertain delayed partial differential equations via sliding mode compensator approach

The distributed sliding mode control (SMC) method of delayed partial differential equations (PDEs)with information of periodical impulse and reaction–diffusion terms (RDTs) is discussed in the article. Firstly, by adopting the sliding mode compensator approach, the switching function including impulsive effects is constructed, which is continuous along the system states. The sliding motion equation is then derived, and its parameters depend on that of sliding mode compensator.Via the direct linear matrix inequality method(DLIM), the exponential stability of sliding motion is analyzed. The proposed distributed SMC strategy can eliminate the impulsive effects and drive the closed-loop state onto a specific sliding manifold in limited time. Finally, a numerical simulation is presented to certify the availability of the proposed scheme.

On the spectral radius properties of a key matrix in periodic impulse control

In this work, we consider the periodic impulse control of a system modeled as a set of linear differential equations. We define a matrix that governs the qualitative behavior of the controlled system. This matrix depends on the period and effects of the control interventions. We investigate properties of the spectral radius of this matrix and in particular, how it depends on the period of the interventions. Our main result is on the convexity of the spectral radius with respect to this period. We discuss implications of this convexity on establishing an optimal and maximum period for effective control. Finally, we provide an example motivated from a real-life scenario.

Exponential Stability of Stochastic Nonlinear Delay Systems Subject to Multiple Periodic Impulses

Exponential Stability of Stochastic Nonlinear Delay Systems Subject to Multiple Periodic Impulses

Asymptotic Properties and Oscillation of the Solutions in a Periodic Impulsive Hematopoiesis Model

Asymptotic Properties and Oscillation of the Solutions in a Periodic Impulsive Hematopoiesis Model

Reinforcement learning for optimal control of linear impulsive systems with periodic impulses

This paper focuses on the finite- and infinite-horizon optimal control problems of linear impulsive systems with periodic impulses under the quadratic performance index. Necessary and sufficient conditions for the optimal impulsive system are derived in terms of hybrid Riccati equations by utilizing the variational method and the collocation method combined with a time-varying Lyapunov function. Different from the existing model-based impulsive control schemes, three reinforcement learning (RL)-based algorithms are proposed to solve the optimal impulsive controller and hybrid controller for the impulsive system without the exact knowledge of the system dynamics. The asymptotical stability of the impulsive control system and the convergence of the RL-based algorithms are proved rigorously. Finally, a numerical simulation illustrates the effectiveness of the proposed control methods.

Compound fault diagnosis of rolling bearings based on AVMD and IMOMEDA

The intricate nature of compound fault diagnosis in rolling bearings during nonstationary operations poses a challenge. To address this, a novel technique combines adaptive variational mode decomposition (AVMD) with improved multipoint optimal minimum entropy deconvolution adjustment (IMOMEDA). The compound fault signal is isolated through AVMD, with internal parameters obtained via a new indicator termed integrated fault-impact measure index guiding the improved dung beetle optimizer. An adaptive selection method, using a weight factor, chooses the intrinsic mode function containing principal fault data. IMOMEDA whose key parameters are determined by a novel combinatorial strategy is then employed to deconvolute selected fault components, enhancing periodic fault impulses by removing complex interferences and ambient noise. The deconvoluted signal undergoes enhanced envelope spectrum processing to extract fault frequencies and identify fault types. Numerical simulations and experimental data confirm the method’s effectiveness and feasibility for compound faults diagnosis of rolling bearings, showcasing its superiority over existing techniques.

An adaptive reweighted-Kurtogram for bearing fault diagnosis under strong external impulse noise

In vibration-based fault diagnosis of rotating machinery, strong impulse noise constitutes a widely encountered source of external interference, thereby posing significant challenges to the effective extraction of diagnostic information. In this context, an adaptive reweighted-Kurtogram (ARKurtogram) method is proposed. The bearing transient fault signatures are accurately extracted through two aspects – that is, precise frequency band division and robust band selection indicator. Specifically, we use the dual-tree complex wavelet packet transform (DTCWPT) as the band division tool and propose the sub-bands rearranged and ensemble DTCWPT which addresses the band disorder problem, yields far richer band division patterns and maintains excellent performance of DTCWPT in signal decomposition. Meanwhile, we introduce a robust indicator characterizing periodic fault impulses to accurately select the fault band. In comparison with the classical kurtosis and the advanced reweighted-kurtosis, this indicator is insensitive to strong external impulse noise and its calculation process contains a sliding window averaging approach which makes the calculation entirely automated without human intervention. The validity of the ARKurtogram is investigated with the analysis of vibration signals measured from fault-injection experiments. The comparisons with the classical fast Kurtogram method and the advanced Autogram method highlight the advantages of the method in extracting bearing transient fault signatures from complex signals with strong external impulse noise. It shows high potential in the application of industrial bearing fault diagnosis.

Difunctional Microelectrode Arrays for Single-Cell Electrical Stimulation and pH Detection.

Due to its direct effect on biomolecules and cells, electrical stimulation (ES) is now widely used to regulate cell proliferation, differentiation, and neurostimulation and is even used in the clinic for pain relief, treatment of nerve damage, and muscle rehabilitation. Conventional ES is mostly studied on cell populations, but the heterogeneity of cancer cells results in the inability to access the response of individual cells to ES. Therefore, detecting the extracellular pH change (ΔpHe) after ES at the single-cell level is important for the application of ES in tumor therapy. In this study, cellular ΔpHe after periodic impulse electrostimulation (IES) was monitored in situ by using a polyaniline (PANI)-modified gold microelectrode array. The PANI sensor had excellent sensitivity (53.68 mV/pH) and linear correlation coefficient (R2 = 0.999) over the pH range of 5.55-7.41. The cells showed different degrees of ΔpHe after the IES with different intervals and stimulation potential. A shorter pulse interval and a higher stimulation potential could effectively enhance stimulation and increase cellular ΔpHe. At 0.5 V potential stimulation, the cellular ΔpHe increased with decreasing pulse interval. However, if the pulse interval was long enough, even at a higher potential of 0.7 V, there was no significant additional ΔpHe due to the insufficient stimulus strength. Based on the above conclusions, the prepared PANI microelectrode arrays (MEAs) were capable of stimulating and detecting single cells, which contributed to the deeper application of ES in tumor therapy.

Amplitude-based multiscale reverse dispersion entropy: a novel approach to bearing fault diagnosis

The multiscale fluctuation dispersion entropy algorithm (MFDE) is widely used to extract the characteristics from a variety of complex nonlinear signals, including bearing signals, due to its excellent performance to quantify the uncertainties of complex nonlinear systems. However, limited by the classification number and coarse-graining process, the periodic impulses generated by the defect point cannot be effectively detected by MFDE, restraining the characterization abilities of entropy features and resulting in undesirable diagnosis results for bearing faults. To overcome the disadvantages of MFDE, an amplitude-based multiscale dispersion entropy (AMDE) is proposed in this paper. The AMDE utilizes the phase scale factor to calculate multiple groups of amplitude difference series that contain different amplitude information. As such, the amplitude compression caused by the large-scale factor in traditional coarse-graining process is avoided, and the calculated entropy features not only characterize the irregularity of the whole signal but also reflect the changes of the impulse components. Afterwards, the perception range and the sensibility of AMDE are expanded and enhanced for amplitude variation, and the coarse-graining process and Gaussian reference are used to obtain multi-dimensional reversed entropy features. Combining those steps, the amplitude-based multiscale reverse dispersion entropy (AMRDE) algorithm is proposed. Finally, the capability of the proposed algorithm to track the amplitude variation and fluctuation is successfully demonstrated by analyzing noisy signals and amplitude-modulated signal. Meanwhile, the features extracted from bearing signals demonstrated that it is effective to use AMRDE to represent the health conditions of rolling bearing. Therefore, the entropy metric calculated by AMRDE can be the useful indicator in the fields of mechanical equipment fault diagnosis, structural health monitoring, and so on.