Gearbox Fault Diagnosis using Adaptive Zero Phase Time-varying Filter Based on Multi-scale Chirplet Sparse Signal Decomposition

When used for separating multi-component non-stationary signals, the adaptive time-varying filter(ATF) based on multi-scale chirplet sparse signal decomposition(MCSSD) generates phase shift and signal distortion. To overcome this drawback, the zero phase filter is introduced to the mentioned filter, and a fault diagnosis method for speed-changing gearbox is proposed. Firstly, the gear meshing frequency of each gearbox is estimated by chirplet path pursuit. Then, according to the estimated gear meshing frequencies, an adaptive zero phase time-varying filter(AZPTF) is designed to filter the original signal. Finally, the basis for fault diagnosis is acquired by the envelope order analysis to the filtered signal. The signal consisting of two time-varying amplitude modulation and frequency modulation(AM-FM) signals is respectively analyzed by ATF and AZPTF based on MCSSD. The simulation results show the variances between the original signals and the filtered signals yielded by AZPTF based on MCSSD are 13.67 and 41.14, which are far less than variances (323.45 and 482.86) between the original signals and the filtered signals obtained by ATF based on MCSSD. The experiment results on the vibration signals of gearboxes indicate that the vibration signals of the two speed-changing gearboxes installed on one foundation bed can be separated by AZPTF effectively. Based on the demodulation information of the vibration signal of each gearbox, the fault diagnosis can be implemented. Both simulation and experiment examples prove that the proposed filter can extract a mono-component time-varying AM-FM signal from the multi-component time-varying AM-FM signal without distortion.

SRMD:Sparse Random Mode Decomposition

Signal decomposition and multiscale signal analysis provide many useful tools for timefrequency analysis.We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram.The randomization is both in the time window locations and the frequency sampling,which lowers the overall sampling and computational cost.The sparsification of the spectrogram leads to a sharp separation between time-frequency clusters which makes it easier to identify intrinsic modes,and thus leads to a new data-driven mode decomposition.The applications include signal representation,outlier removal,and mode decomposition.On benchmark tests,we show that our approach outperforms other state-of-the-art decomposition methods.

Decomposition of Surface Electromyographic Signal Using Hidden Markov Model

The detection of physiological signals from the motor system （electromyographic signals） is being utilized in the practice clinic to guide the therapist in a more precise and accurate diagnosis of motor disorders. In this context, the process of decomposition of EMG （electromyographic） signals that includes the identification and classification of MUAP （Motor Unit Action Potential） of a EMG signal, is very important to help the therapist in the evaluation of motor disorders. The EMG decomposition is a complex task due to EMG features depend on the electrode type （needle or surface）, its placement related to the muscle, the contraction level and the health of the Neuromuscular System. To date, the majority of researches on EMG decomposition utilize EMG signals acquired by needle electrodes, due to their advantages in processing this type of signal. However, relatively few researches have been conducted using surface EMG signals. Thus, this article aims to contribute to the clinical practice by presenting a technique that permit the decomposition of surface EMG signal via the use of Hidden Markov Models. This process is supported by the use of differential evolution and spectral clustering techniques. The developed system presented coherent results in： （1） identification of the number of Motor Units actives in the EMG signal; （2） presentation of the morphological patterns of MUAPs in the EMG signal; （3） identification of the firing sequence of the Motor Units. The model proposed in this work is an advance in the research area of decomposition of surface EMG signals.

Rolling Bearing Feature Frequency Extraction using Extreme Average Envelope Decomposition

The vibration signal contains a wealth of sensitive information which reflects the running status of the equipment. It is one of the most important steps for precise diagnosis to decompose the signal and extracts the effective information properly. The traditional classical adaptive signal decomposition method, such as EMD, exists the problems of mode mixing, low decomposition accuracy etc. Aiming at those problems, EAED（extreme average envelope decomposition） method is presented based on EMD. EAED method has three advantages. Firstly, it is completed through midpoint envelopment method rather than using maximum and minimum envelopment respectively as used in EMD. Therefore, the average variability of the signal can be described accurately. Secondly, in order to reduce the envelope errors during the signal decomposition, replacing two envelopes with one envelope strategy is presented. Thirdly, the similar triangle principle is utilized to calculate the time of extreme average points accurately. Thus, the influence of sampling frequency on the calculation results can be significantly reduced. Experimental results show that EAED could separate out single frequency components from a complex signal gradually. EAED could not only isolate three kinds of typical bearing fault characteristic of vibration frequency components but also has fewer decomposition layers. EAED replaces quadratic enveloping to an envelope which ensuring to isolate the fault characteristic frequency under the condition of less decomposition layers. Therefore, the precision of signal decomposition is improved.

ALGORITHM FOR THE DETECTION AND PARAMETER ESTIMATION OF MULTICOMPONENT LFM SIGNALS

A novel algorithm based on Radon-Ambiguity Transform (RAT) and Adaptive Signal Decomposition (ASD) is presented for the detection and parameter estimation of multicompo-nent Linear Frequency Modulated (LFM) signals. The key problem lies in the chirplet estimation. Genetic algorithm is employed to search for the optimization parameter of chirplet. High estimation accuracy can be obtained even at low Signal-to-Noisc Ratio(SNR). Finally simulation results are provided to demonstrate the performance of the proposed algorithm.

A hybrid decomposition-boosting model for short-term multi-step solar radiation forecasting with NARX neural network

Due to global energy depletion,solar energy technology has been widely used in the world.The output power of the solar energy systems is affected by solar radiation.Accurate short-term forecasting of solar radiation can ensure the safety of photovoltaic grids and improve the utilization efficiency of the solar energy systems.In the study,a new decomposition-boosting model using artificial intelligence is proposed to realize the solar radiation multi-step prediction.The proposed model includes four parts:signal decomposition(EWT),neural network(NARX),Adaboost and ARIMA.Three real solar radiation datasets from Changde,China were used to validate the efficiency of the proposed model.To verify the robustness of the multi-step prediction model,this experiment compared nine models and made 1,3,and 5 steps ahead predictions for the time series.It is verified that the proposed model has the best performance among all models.

Empirical Wavelet Transform;Stationary and Nonstationary Signals

Signal decomposition into the frequency components is one of the oldest challenges in the digital signal processing.In early nineteenth century,Fourier transform(FT)showed that any applicable signal can be decomposed by unlimited sinusoids.However,the relationship between time and frequency is lost under using FT.According to many researches for appropriate time-frequency representation,in early twentieth century,wavelet transform(WT)was proposed.WT is a well-known method which developed in order to decompose a signal into frequency components.In contrast with original WT which is not adaptive according to the input signal,empirical wavelet transform(EWT)was proposed.In this paper,the performance of discrete WT(DWT)and EWT in terms of signal decomposing into basic components are compared.For this purpose,a stationary signal including five sinusoids and ECG as biomedical and nonstationary signal are used.Due to being non-adaptive,DWT may remove signal components but EWT because of being adaptive is appropriate.EWT can also extract the baseline of ECG signal easier than DWT.

Noise level estimation method with application to EMD-based signal denoising

This paper proposes a new signal noise level estimation approach by local regions. The estimated noise variance is applied as the threshold for an improved empirical mode decomposition（EMD） based signal denoising method. The proposed estimation method can effectively extract the candidate regions for the noise level estimation by measuring the correlation coefficient between noisy signal and a Gaussian filtered signal. For the improved EMD based method, the situation of decomposed intrinsic mode function（IMFs） which contains noise and signal simultaneously are taken into account. Experimental results from two simulated signals and an X-ray pulsar signal demonstrate that the proposed method can achieve better performance than the conventional EMD and wavelet transform（WT） based denoising methods.

Health monitoring of time-varying stochastic structures by latent components and fuzzy expert system

In this paper, a novel parametric model-based decomposition method is proposed for structural health monitoring of time-varying structures. For this purpose, the advanced Functional-Series Time-dependent Auto Regressive Moving Average （FS-TARMA） technique is used to estimate the parameters and innovation variance used in the parametric signal decomposition scheme. Additionally, a unique feature extraction and reduction method based on the decomposed signals, known as Latent Components （LCs）, is proposed. To evaluate the efficiency of the proposed method, numerical simulation and an experimental study in the laboratory were conducted on a time-varying structure, where various types of damage were introduced. The Fuzzy Expert System （FES） was used as a classification toot to demonstrate that the proposed method successfully identifies different structural conditions when compared with other methods based on non-reduced and ordinary feature extraction.

Parametric adaptive time-frequency representation based on time-sheared Gabor atoms

A localized parametric time-sheared Gabor atom is derived by convolving a linear frequency modulated factor, modulating in frequency and translating in time to a dilated Gaussian function, which is the generalization of Gabor atom and is more delicate for matching most of the signals encountered in practice, especially for those having frequency dispersion characteristics. The time-frequency distribution of this atom concentrates in its time center and frequency center along energy curve, with the curve being oblique to a certain extent along the time axis. A novel parametric adaptive time-frequency distribution based on a set of the derived atoms is then proposed using a adaptive signal subspace decomposition method in frequency domain, which is non-negative time-frequency energy distribution and free of cross-term interference for multicomponent signals. The results of numerical simulation manifest the effectiveness of the approach in time-frequency representation and signal de-noising processing.

Probability distribution of wind power volatility based on the moving average method and improved nonparametric kernel density estimation

In the process of large-scale,grid-connected wind power operations,it is important to establish an accurate probability distribution model for wind farm fluctuations.In this study,a wind power fluctuation modeling method is proposed based on the method of moving average and adaptive nonparametric kernel density estimation(NPKDE)method.Firstly,the method of moving average is used to reduce the fluctuation of the sampling wind power component,and the probability characteristics of the modeling are then determined based on the NPKDE.Secondly,the model is improved adaptively,and is then solved by using constraint-order optimization.The simulation results show that this method has a better accuracy and applicability compared with the modeling method based on traditional parameter estimation,and solves the local adaptation problem of traditional NPKDE.

Improved Multi-Bandwidth Mode Manifold for Enhanced Bearing Fault Diagnosis

Variational mode decomposition(VMD) has been proved to be useful for extraction of fault-induced transients of rolling bearings. Multi-bandwidth mode manifold(Triple M, TM) is one variation of the VMD, which units multiple fault-related modes with different bandwidths by a nonlinear manifold learning algorithm named local tangent space alignment(LTSA). The merit of the TM method is that the bearing fault-induced transients extracted contain low level of in-band noise without optimization of the VMD parameters. However, the determination of the neighborhood size of the LTSA is time-consuming, and the extracted fault-induced transients may have the problem of asymmetry in the up-and-down direction. This paper aims to improve the efficiency and waveform symmetry of the TM method.Specifically, the multi-bandwidth modes consisting of the fault-related modes with different bandwidths are first obtained by repeating the recycling VMD(RVMD) method with different bandwidth balance parameters. Then, the LTSA algorithm is performed on the multi-bandwidth modes to extract their inherent manifold structure, in which the natural nearest neighbor(Triple N, TN) algorithm is adopted to efficiently and reasonably select the neighbors of each data point in the multi-bandwidth modes. Finally, a weight-based feature compensation strategy is designed to synthesize the low-dimensional manifold features to alleviate the asymmetry problem, resulting in a symmetric TM feature that can represent the real fault transient components. The major contribution of the improved TM method for bearing fault diagnosis is that the pure fault-induced transients are extracted efficiently and are symmetrical as the real. One simulation analysis and two experimental applications in bearing fault diagnosis validate the enhanced performance of the improved TM method over the traditional methods. This research proposes a bearing fault diagnosis method which has the advantages of high efficiency, good waveform symmetry and enhanced in-band noise removal capability.

Unintentional modulation microstructure enlargement

Radio frequency fingerprinting(RFF)is a technology that identifies the specific emitter of a received electromagnetic signal by external measurement of the minuscule hardware-level,device-specific imperfections.The RFF-related information is mainly in the form of unintentional modulation(UIM),which is subtle enough to be effectively imperceptible and is submerged in the intentional modulation(IM).It is necessary to minimize the influence of the IM and expand the slight differences between emitters for successful RFF.This paper proposes a UIM microstructure enlargement(UMME)method based on feature-level adaptive signal decomposition(ASD),accompanied by autocorrelation and cross-correlation analysis.The common IM part is evaluated by analyzing a newly-defined benchmark feature.Three different indexes are used to quantify the similarity,distance,and dependency of the RFF features from different devices.Experiments are conducted based on the real-world signals transmitted from 20 of the same type of radar in the same working mode.The visual image qualitatively shows the magnification of feature differences;different indicators quantitatively describe the changes in features.Compared with the original RFF feature,recognition results based on the Gaussian mixture model(GMM)classifier further validate the effectiveness of the proposed algorithm.

Forecasting wind speed using a reinforcement learning hybrid ensemble model:a high-speed railways strong wind signal prediction study in Xinjiang,China

Considering the application of wind-forecasting technology along the railway,it becomes an effective means to reduce the risk of tain more reliable wind-speed prediction results,this study proposes an intelligent ensemble forecasting method for strong winds train derailment and overturning.Accurate prediction of crosswinds can provide scientific guidance for safe train operation.To obalong the high-speed railway.The method consists of three parts:the data preprocessing module,the hybrid prediction module and original wind speed data.Then,Broyden-Fletcher-Goldfarb-Shanno(BFGS)method,non-linear autoregressive network with exoge-the reinforcement learing ensemble module.First,fast ensemble empirical model decomposition(FEEMD)is used to process the prediction models for all the sublayers of decomposition.Finally,Q-learning is utilized to iteratively calculate the combined weights nous inputs(NARX)and deep belief network(DBN),three benchmark predictors with different characteristics are employed to build of the three models,and the prediction results of each sublayer are superimposed to obtain the model output.The real wind speed data of two railway stations in Xinjiang are used for experimental comparison.Experiments show that compared with the single benchmark model,the hybrid ensemble model has better accumacy and robustness for wind speed prediction along the railway.The 1-step forecasting results mean absolute error(MAE),mean absolute percentage error(MAPE)and root mean square error(RMSE)of Q-leaming-FEEMD-BFGS-NARX-DBN in site #1 and site #2 are 0.0894 m/s,0.6509%,0.1146 m/s,and 0.0458 m/s.0.2709%,0.0616 m/s.respectively.The proposed ensemble model is a promising method for railway wind speed prediction.

Modal identification based on Hilbert-Huang Transform of structural response with S VD preprocessing

In recent years, Empirical mode decomposition and Hilbert spectral analysis have been combined to identify system parameters. Singular-Value Decomposition is pro- posed as a signal preprocessing technique of Hilbert-Huang Transform to extract modal parameters for closely spaced modes and low-energy components. The proposed method is applied to a simulated airplane model built in Automatic Dynamic Analysis of Mechanical Systems software. The results demonstrate that the identified modal parameters are in good agreement with the baseline model.

Research on Non Intrusive Intelligent Monitoring System for Elevator State

The current elevator status monitoring systems basically realize the monitoring of elevator status by collecting signals from the main board of the elevator.However it is costly and lacks universality,which also requires invasive installation.To address the above problems,a non-invasive intelligent monitoring method is proposed in this paper for elevator operation status.Themethod decomposes the acceleration signal into vertical and horizontal components,estimates the dynamics of the elevator using Kalman filter,performs vibration analysis on the horizontal components,establishes a baseline for normal operation,and automatically calibrates the sensors by combining the operating characteristics of the elevator.The traceless Kalman filter based on fused SLAM was performed to couple the sensor information and track the real-time position of the elevator.The effectiveness and robustness of the method are verified in actual operation,and the problem of elevator position error accumulation is basically solved without installing fiducials.The designed non-intrusive elevator status intelligent monitoring method is low-cost and universal,which is of practical significance for promoting on-demand elevator maintenance.

Extracting outer function part from Hardy space function

Any analytic signal fa(e^(it)) can be written as a product of its minimum-phase signal part(the outer function part) and its all-phase signal part(the inner function part). Due to the importance of such decomposition, Kumarasan and Rao(1999), implementing the idea of the Szeg?o limit theorem(see below),proposed an algorithm to obtain approximations of the minimum-phase signal of a polynomial analytic signal fa(e^(it)) = e^(iN0t)M∑k=0a_k^(eikt),(0.1)where a_0≠ 0, a_M≠ 0. Their method involves minimizing the energy E(f_a, h_1, h_2,..., h_H) =1/(2π)∫_0^(2π)|1+H∑k=1h_k^(eikt)|~2|fa(e^(it))|~2dt(0.2) with the undetermined complex numbers hk's by the least mean square error method. In the limiting procedure H →∞, one obtains approximate solutions of the minimum-phase signal. What is achieved in the present paper is two-fold. On one hand, we rigorously prove that, if fa(e^(it)) is a polynomial analytic signal as given in(0.1),then for any integer H≥M, and with |fa(e^(it))|~2 in the integrand part of(0.2) being replaced with 1/|fa(e^(it))|~2,the exact solution of the minimum-phase signal of fa(e^(it)) can be extracted out. On the other hand, we show that the Fourier system e^(ikt) used in the above process may be replaced with the Takenaka-Malmquist(TM) system, r_k(e^(it)) :=((1-|α_k|~2e^(it))/(1-α_ke^(it))^(1/2)∏_(j=1)^(k-1)(e^(it)-α_j/(1-α_je^(it))^(1/2), k = 1, 2,..., r_0(e^(it)) = 1, i.e., the least mean square error method based on the TM system can also be used to extract out approximate solutions of minimum-phase signals for any functions f_a in the Hardy space. The advantage of the TM system method is that the parameters α_1,..., α_n,...determining the system can be adaptively selected in order to increase computational efficiency. In particular,adopting the n-best rational(Blaschke form) approximation selection for the n-tuple {α_1,..., α_n}, n≥N, where N is the degree of the given rational analytic signal, the minimum-phase part of a rational analytic signal can be accurately and efficiently extracted out.