Strong White Noise Research Articles

Generalized Shannon entropy sparse wavelet packet transform for fault detection of traction motor bearings in high-speed trains

An effective structural health monitoring method of traction motor bearings is a powerful guarantee for the safety operation of high-speed trains. However, it is exceptionally difficult to detect bearing fault characteristics from the vibration signals of traction motor bearings operating at high rotational speeds. In this scenario, a generalized Shannon entropy sparse wavelet packet transform (GSWPT) for fault detection of motor bearings is proposed in this paper. Firstly, a generalized Shannon entropy sparse regularization method is proposed to obtain sparse wavelet reconstruction coefficients by extending the definition of the Shannon information entropy, and the non-convex sparse regularization function is minimized by synergistic swarm optimization algorithm. Then, the wavelet node coefficients are weighted according to the second-order cyclostationarity index of the wavelet packet node to further enhance the sparsity of the reconstructed signal. Moreover, the optimal decomposition level of GSWPT is adaptively selected by the maximum sparsity and cyclostationarity criterion. Particularly, in order to verify the bearing fault detection performance of GSWPT in practical engineering, a bearing fault dynamic model of traction motor in high-speed train was established based on Hertz contact theory and the fourth-order Runge-Kutta method to obtain simulated data under strong Gaussian white noise, and a corresponding test platform was constructed to collect experimental data under different operating conditions. Finally, the applications on the simulated and experimental signals of traction motor bearings in high-speed trains demonstrate that GSWPT significantly outperforms the conventional wavelet packet transform, dual-tree complex wavelet packet transform, blind deconvolution, modal decomposition, and Infogram methods to some extent for fault detection.

The LESGIRgram: A New Method to Select the Optimal Demodulation Frequency Band for Rolling Bearing Faults

Resonance demodulation of vibration signals is a common method for extracting fault information from rolling bearings. Nonetheless, demodulation quality is dependent on frequency band location. Established methods such as the Fast Kurtogram, Autogram, SKRgram, etc. have achieved satisfactory results in some cases, but the results are not good in the presence of strong white Gaussian noise and random impulses. To solve these issues, an algorithm that selects the optimal demodulation frequency band (ODFB) based on the ratio of the logarithmic envelope spectrum Gini coefficient (LESGIRgram) is proposed. The core idea of this paper is to capture the difference between the LESGIgrams of health and fault signals and accordingly locate the frequency bands that contain the most fault information. Initially, the baseline is constructed by calculating the logarithmic envelope spectrum Gini coefficient matrix of the health bearing (LESGIbaseline). Next, the LESGI matrix of the fault bearing (LESGImeasured) is computed. The ratio of LESGImeasured to LESGIbaseline is calculated, and the ODFB can be selected with the maximum LESGIR. The fault signal is then filtered using this derived ODFB, and envelope analysis is performed to extract fault features. The proposed algorithm for detecting rolling bearing faults has been verified for accuracy and effectiveness through simulation and experimental data.

A Reinforced Noise Resistant Correlation Method for Bearing Condition Monitoring

Condition monitoring plays a significant role in guaranteeing the reliability and safety of rotating machinery, which aims to detect an incipient fault and assess the degradation tendency. The construction of a health index (HI) is a crucial step to realize above tasks. At present, kurtosis, crest factor, and so on have been recognized as popular HIs to depict the operating condition. However, shortcomings of these classical HIs still exist: 1) classical HIs are prone to be affected by strong white Gaussian noise; 2) classical HIs are not sensitive to incipient faults. To deal with these two shortcomings, a reinforced noise resistant correlation method is proposed in this paper. Firstly, a new signal is constructed using the steps of segmenting and averaging to suppress the interference of noise. Then, a novel correlation function is used to get the hidden period. The proposed HI is constructed based on the discrete version of this correlation function to increase the sensitivity of incipient faults. Subsequently, theoretical values of the proposed HI under healthy states are investigated. The effectiveness of the method is demonstrated using simulated degradation processes and two accelerated degradation datasets of rolling element bearings. Through comparisons with other classical HIs, the proposed HI can simultaneously suppress the interference of strong noise and detect incipient faults. The comparison results identify the effectiveness of the proposed method in monitoring the condition of rotating machinery. Note to Practitioners—This work aims to provide a novel health index construction method for rotating machinery condition monitoring. The key issues involved in this problem include 1) how to capture the complex relationship between the measured vibration signals and the underlying health condition of rotating machinery; 2) how to suppress the interference of environmental noise. The novelty of this work is that it develops a method for condition monitoring considering the measured signals with strong white Gaussian noise. It properly captures the complex relationship between measured signals and the underlying health condition. There are four main steps to implement this approach: 1) collecting the vibration signals from rotating machinery; 2) constructing new periodic signal to suppress the interference of strong background noise; 3) constructing novel correlation functions to establish the relationship between the vibration signals and the underlying health condition of the rotating machine; 4) modeling the HI. A simulation and two real cases of the bearing degradation process are used to show that the proposed HI can simultaneously suppress the interference of strong noise and detect the incipient faults compared with some classical HI construction methods. In the future, the problem of how to address the measured signals contaminated by non-Gaussian noise and the machinery containing compound faults should be solved to extend this method in a complex system.

A 1/f Noise Detection Method for IGBT Devices Based on PSO-VMD

The generation of 1/f noise is closely related to the quality defects of IGBT devices. In the process of detecting single-tube noise of IGBT, thermal noise and shot noise show obvious white noise characteristics in the low-frequency range. This paper investigates how to accurately detect the 1/f noise under strong white noise, and thus proposes a particle swarm optimization method known as variational mode decomposition. First, the particle swarm optimization algorithm was used twice to search the optimal parameter combination between the penalty parameter and the decomposition modulus of the VMD model. Then, the parameters of the variational mode decomposition algorithm were set in optimal parameter combination. The frequency center and bandwidth of each IMF component were determined by continuous iteration in the variational framework. Finally, the 1/f noise signal was adaptively separated from background noise. Extensive experimental investigations carried out under different signal-to-noise ratios, compared with the optimal wavelet denoising algorithm, revealed that the PSO-VMD algorithm improved the signal-to-noise ratio by 6.6%, 16.82%, and 42.48%, whereas the mean square error is reduced by 7.12%, 19.80%, and 33.76%.

A Quantum Weak Signal Detection Method for Strengthening Target Signal Features under Strong White Gaussian Noise

As the noise power increases, the target signal features become less obvious, which leads to the failure of weak signal detection methods. To address this problem, a quantum weak signal detection method, Local Semi-Classical Signal Analysis-Singular Value Decomposition (LSCSA-SVD), for strengthening target signal features under strong white Gaussian noise is proposed. Firstly, the time domain weak signal is quantized by the Schrodinger operator and its discrete spectrum formula. Then, in the quantum domain, the later eigenvalues are used to reconstruct the time domain signal, which can protect and enhance the target signal features. Finally, the difference between signal and noise in the singular value vector is used to further extract the reconstruction signal features. In simulation, the LSCSA-SVD can accurately extract target signals from white Gaussian noise signals with a signal-to-noise ratio (SNR) of −30 dB, which is better than the comparison methods. In the experiment, the weak acceleration sensor signal and the weak signal of the test circuit are successfully extracted. The results show that the LSCSA-SVD can suppress strong noise and improve the SNR.

An Approach to 1/f Noise Detection Based on Adaptive T-ATFPF Algorithm

The generation of 1/f noise is closely related to the quality defects of IGBT devices. In the process of detecting IGBT single tube noise, thermal noise and shot noise show obvious white noise characteristics in the low frequency band, which are detected under the background of strong white noise 1/f noise can characterize the performance of IGBT devices. Therefore, on the basis of the Time-Frequency Peak Filtering (TFPF) algorithm, a two-dimensional time-domain adaptive T-ATFPF algorithm is proposed, and the adaptive segmentation is realized by means of the confidence interval crossing criterion based on Chebyshev’s inequality. Variable window length,use a small window length to process the signal section, which retains more detailed information of the effective signal.Use a larger window length to process the buffer section to ensure a smooth transition.Use the large window length to process the noise section, which more effectively suppresses randomness for noise, apply T-ATFPF to artificial synthesis model and actual model. Experimental results indicate that compared with the conventional algorithm, the improved method can better recover 1/f noise, and the ratio of signal to noise is greatly improved by about 1.3dB.

Optimal environmental estimation with ocean ambient noise.

This article presents an asymptotically optimal technique for estimating environmental parameters from ocean ambient noise. Noise from wind and breaking waves propagates through the water column and reflects off the bottom over a wide range of angles and frequencies and, in doing so, imparts information about the environment to the noise covariance matrix for a receiver array. Most environmental estimation techniques focus on spatial filtering methods aimed at recovering the vertical noise directionality. However, an often overlooked fact is that the noise covariance matrix fully characterizes the probability density function of each snapshot, which forms the basis for an information-theoretic approach. In this light, it is possible to obtain the theoretical bounds on optimal estimator performance while also providing a basis for assessing the utility of different parameterization schemes. Most importantly, it provides a natural definition for a maximum likelihood estimator that meets the optimal bounds in an asymptotic sense. This technique outperforms beamforming-based methods by a significant margin. It also remains unbiased in the presence of strong white noise, is tolerant to array tilt, can operate beyond the array design frequency, but does suffer greater sensitivity to model mismatch. These trade-offs are explored with simulations and analyses of experimental data.

Functional time series model identification and diagnosis by means of auto- and partial autocorrelation analysis

Quantifying the serial correlation across time lags is a crucial step in the identification and diagnosis of a time series model. Simple and partial autocorrelation functions of the time series are the most widely used tools for this purpose with scalar time series. Nevertheless, there is a lack of an established method for the identification of functional time series (FTS) models. Functional versions of the autocorrelation and partial autocorrelation functions for FTS based on the L2 norm of the lagged autocovariance operators of the series are proposed. Diagnostic plots of these functions coupled with prediction bounds derived from large sample results for the autocorrelation and partial autocorrelation functions estimated from a strong functional white noise series are proposed as fast and efficient tools for selecting the order and assessing the adequacy of functional SARMAX models. These methods are studied in numerical simulations with both white noise and serially correlated functional processes, which show that the structure of the processes can be well identified using the proposed techniques. The applicability of the method is illustrated with two real-world datasets: Eurodollar futures contracts and electricity price profiles.

Upper Semicontinuity of Random Attractor for a Kirchhoff Type Suspension Bridge Equation with Strong Damping and White Noise

This paper is devoted to the well-posedness and long-time behavior of a stochastic Kirchhoff type suspension bridge equation with strong damping. The existence of the random attractor for a Kirchhoff type suspension bridge equation with white noise is established. Moreover, the upper semicontinuity of random attractors is also provided when the coefficient of random term approaches zero.

A general white noise test based on kernel lag-window estimates of the spectral density operator

A general white noise test for functional time series is considered. The idea of the test is to estimate a distance between the spectral density operator of a weakly stationary time series and the constant spectral density operator of an uncorrelated time series. The estimator of the distance is based on a kernel lag-window type estimator of the spectral density operator. When the observed time series is a strong white noise in a real separable Hilbert space, it is shown that the asymptotic distribution of the test statistic is standard normal, and it is further shown that the test statistic diverges for general serially correlated time series. These results recover as special cases some previous tests. In order to implement the test, a number of kernel and bandwidth choices is proposed and studied, including a new data adaptive bandwidth, as well as data adaptive power transformations of the test statistic that improve the normal approximation in finite samples. A simulation study demonstrated that the proposed method has good size and improved power when compared to other methods available in the literature, while also offering a light computational burden.

Detection for Incipient Damages of Wind Turbine Rolling Bearing Based on VMD-AMCKD Method

Incipient damages of wind turbine rolling bearing are very difficult to be detected because of the interference of multi-frequency components and strong ambient noise. To solve this problem, this paper proposes a new detected method named VMD-AMCKD, combining complementary advantages of variational mode decomposition (VMD) and adaptive maximum correlated kurtosis deconvolution (AMCKD). A novel index is proposed to screen out the most sensitive mode containing fault information after VMD decomposition. The mode also can determine a suspectable range for the fault frequency, based on which the optimized range of devolution period T in MCKD can be pre-determined. The Grasshopper optimization algorithm (GOA) is adapted to adaptively select the key parameters in MCKD. The proposed method can successfully diagnose the simulated signal mixed with strong white Gaussian noise. Its robustness is further proven by the diagnosis for three different types of experimental signal from CWRU bearing data center. Finally, the VMD-AMCKD is applied to detect incipient damages of rolling bearings in a laboratory wind turbine.

A Noise Resistant Correlation Method for Period Detection of Noisy Signals

This paper develops a novel method called the noise resistant correlation method for detecting the hidden period from the contaminated (noisy) signals with strong white Gaussian noise. A novel correlation function is proposed based on a newly constructed periodic signal and the contaminated signal to effectively detect the target hidden period. In contrast with the conventional autocorrelation analysis (AUTOC) method, this method demonstrates excellent performance, especially when facing strong noise. Fault diagnoses of rolling element bearings and gears are presented as application examples and the performance of the proposed method is compared with that of the AUTOC method.

Inference for the autocovariance of a functional time series under conditional heteroscedasticity

Most methods for analyzing functional time series rely on the estimation of lagged autocovariance operators or surfaces. As in univariate time series analysis, testing whether or not such operators are zero is an important diagnostic step that is well understood when the data, or model residuals, form a strong white noise. When functional data are constructed from dense records of, for example, asset prices or returns, a weak white noise model allowing for conditional heteroscedasticity is often more realistic. Applying inferential procedures for the autocovariance based on a strong white noise to such data often leads to the erroneous conclusion that the data exhibit significant autocorrelation. We develop methods for performing inference for the lagged autocovariance operators of stationary functional time series that are valid under general conditional heteroscedasticity conditions. These include a portmanteau test to assess the cumulative significance of empirical autocovariance operators up to a user selected maximum lag, as well as methods for obtaining confidence bands for a functional version of the autocorrelation that are useful in model selection/validation. We analyze the efficacy of these methods through a simulation study, and apply them to functional time series derived from asset price data of several representative assets. In this application, we found that strong white noise tests often suggest that such series exhibit significant autocorrelation, whereas our tests, which account for functional conditional heteroscedasticity, show that these data are in fact uncorrelated in a function space.

Formation and disruption of tonotopy in a large-scale model of the auditory cortex.

There is ample experimental evidence describing changes of tonotopic organisation in the auditory cortex due to environmental factors. In order to uncover the underlying mechanisms, we designed a large-scale computational model of the auditory cortex. The model has up to 100 000 Izhikevich's spiking neurons of 17 different types, almost 21 million synapses, which are evolved according to Spike-Timing-Dependent Plasticity (STDP) and have an architecture akin to existing observations. Validation of the model revealed alternating synchronised/desynchronised states and different modes of oscillatory activity. We provide insight into these phenomena via analysing the activity of neuronal subtypes and testing different causal interventions into the simulation. Our model is able to produce experimental predictions on a cell type basis. To study the influence of environmental factors on the tonotopy, different types of auditory stimulations during the evolution of the network were modelled and compared. We found that strong white noise resulted in completely disrupted tonotopy, which is consistent with in vivo experimental observations. Stimulation with pure tones or spontaneous activity led to a similar degree of tonotopy as in the initial state of the network. Interestingly, weak white noise led to a substantial increase in tonotopy. As the STDP was the only mechanism of plasticity in our model, our results suggest that STDP is a sufficient condition for the emergence and disruption of tonotopy under various types of stimuli. The presented large-scale model of the auditory cortex and the core simulator, SUSNOIMAC, have been made publicly available.

Existence of random attractors for the floating beam equation with strong damping and white noise

In this paper, we investigate the existence of a compact random attractor for the random dynamical system generated by a model for nonlinear oscillations in a floating beam equation with strong damping and white noise.

A Novel Denoising Method Based on Ensemble Empirical Mode Decomposition – Principle Component Analysis

Equipment performance degradation model is a key component in its diagnosis and prognosis models. As to slewing bearing, vibration signals are usually non-stationary and with strong white noise, which makes it very difficult to extract useful information from the signals. Therefore, an Ensemble Empirical Mode Decomposition – Principle Component Analysis (EEMD - PCA) based method was proposed to denoise the vibration signals and performance degradation model was established by PCA. To verify the proposed method, an experiment was conducted and the life cycle vibration signals were acquired. After denoising, performance degradation model was established to explain the denoising performance. Results show that the proposed method acquired a better denoising performance than EEMD-MSPCA, which provides a potential for further research.

Linear bootstrap methods for vector autoregressive moving-average models

We provide the theoretical justification of bootstrapping stationary invertible echelon vector autoregressive moving-average (VARMA) models using linear methods. The asymptotic validity of the bootstrap is established with strong white noise under parametric and nonparametric assumptions. Our methods are practical and useful for building reliable simulation-based inference and forecasting without implementing nonlinear estimation techniques such as ML which is usually burdensome, time demanding or impractical, particularly in big or highly persistent systems. The relevance of our procedures is more pronounced in the context of dynamic simulation-based techniques such as maximized Monte Carlo (MMC) tests [see Dufour J-M. Monte Carlo tests with nuisance parameters: a general approach to finite-sample inference and nonstandard asymptotics in econometrics. J Econom. 2006;133(2):443–477 and Dufour J-M, Jouini T. Finite-sample simulation-based tests in VAR models with applications to Granger causality testing. J Econom. 2006;135(1–2):229–254 for the VAR case]. Simulation evidence shows that, compared with conventional asymptotics, our bootstrap methods have good finite-sample properties in approximating the actual distribution of the studentized echelon VARMA parameter estimates, and in providing echelon parameter confidence sets with satisfactory coverage.

Smooth Sliding Mode Control for Trajectory Tracking of Greenhouse Spraying Mobile Robot

For the spraying mobile robot working in greenhouse, due to the inconsistency of drive motors and the rough walking surface, it is easy to track off. For the liquidity of pesticide, the load always changes even the speed jumps. Because of these uncertainties, external disturbances and the difficulty of constructing the system dynamic model, it is hard to implement the trajectory tracking control of the spraying mobile robot steadily, precisely and quickly. In order to solve the problem, a smooth sliding mode trajectory tracking control method is proposed based on the distribute control strategy for each branch. Moreover, its stability is proved using the Lyapunov function. The simulation results show that the proposed method can track the reference trajectories precisely, quickly and steadily under the strong white noise. The chattering phenomenon of the control law is restrained compared to the conventional sliding mode control. The trajectory tracking performance is better than that of the fuzzy control. The designed method is easy to realize and doesn’t need to construct the precise mathematical model, so, it affords an economical and convenient control method for solving the trajectory tracking problem of the greenhouse spraying mobile robot under various uncertain interferences. DOI: http://dx.doi.org/10.11591/telkomnika.v11i2.1988

PHOTOACOUSTIC SIGNALS DENOISING BASED ON EMPIRICAL MODE DECOMPOSITION AND ENERGY-WINDOW METHOD

In the process of photoacoustic imaging (PAI), the photoacoustic signals are polluted by a strong background white noise, which is caused by many factors such as the system thermal noise or short noise, the tissue reflecting or scattering interference, and the impedance match lack between the transducer and tissue. The inevitable noise can degrade the contrast sensitivity of photoacoustic images seriously. In this paper, based on the energy window, a CMSE-EMD denoising method is employed to photoacoustic image reconstruction. Results of the simulation demonstrate that it can eliminate the image artifacts more effectively and achieve great improvement in image quality.

Fault Discrimination Using Synchronized Sequence Measurements under Strong White Gaussian Noise Background

In this paper on strong white Gaussian noise background based on discriminant analysis theory, we mainly adopt synchronized sequence measurements of PMU to search for laws of electrical quantities marked changes. We have developed a method to quickly and accurately discriminate fault components and fault sections. The research has shown that the fault discrimination by discriminant analysis theory is effective and reliable. Under the interference of strong random white Gaussian noise, discriminant analysis still has high redundancy.