Random Impulses Research Articles

Finite-Time Stochastic Stability of Random Impulsive Positive System

The paper focuses on the finite-time stochastic stability (FTSS) problems for positive system with random impulses. Combining Lyapunov functions with the probability property of the impulsive interval, first, the sufficient conditions of FTSS for the positive systems affected by one type of random impulses are given; second, the criteria of FTSS for positive systems suffered from multiple types of random impulses are established. Finally, two examples are presented to show the validity of results.

Exponential stabilization of fixed and random time impulsive delay differential system with applications.

In this work, we study the problem of p-th moment global exponential stability for functional differential equations and scalar chaotic delayed equations under random impulsive effects. Meanwhile, the p-th moment global exponential synchronization for the proposed equations is also discussed, whereas the main results are proved by using Lyapunov function and Razumikhin technique. Furthermore, the impact of fixed and random time impulses are presented by applying the results to Mackey Glass blood cell production model and Ikeda bistable resonator model. Finally, the effectiveness of fixed and random impulses are depicted via graphical representations.

Existence and Ulam-Hyers-Rassias stability of stochastic differential equations with random impulses

In this paper, we investigate the existence and Ulam-Hyers-Rassias stability of solutions for stochastic differential equations with random impulses. Based on the Krasnoselskii?s fixed point theorem, we perform investigations on the existence of solutions to the system of stochastic differential equations with random impulses. We apply the integral inequality of Gronwall type to the equations and study their Ulam-Hyers-Rassias stability.

Adaptive Morphological Analysis Method and Its Application for Bearing Fault Diagnosis

The vibration response of faulty bearing is always characterized by periodic transient impulses in the signal. Generally, these fault-related features are inevitably submerged in noise and harmonic components. Mathematical morphology is an excellent method of noise reduction, which can retain the detail information of impulses in the time domain. However, the filtering effect of traditional morphological operator (MO) might be easily affected by random impulses, and the proper selection of the structure element (SE) depends heavily on the experience of researchers. In order to effectively remove these interferences and extract the fault features accurately, an improved method, named adaptive morphological filter (AMF), is proposed in this article. This method utilizes autocorrelation to lift MO in time domain to enhance periodic components, and the scale of SE can, therefore, be calculated with the local maximum of the autocorrelation spectrum. Since the selection of the optimal SE scale is adaptive, researchers’ experience is no longer needed, and there is also no need to calculate the fault characteristic frequency (FCF) for the determination of maximum scale of SE. The vibration and acoustical signals of faulty locomotive wheel set bearing are analyzed with this method, and the results verify its effectiveness and ability.

EXISTENCE AND EXPONENTIAL STABILITY OF MILD SOLUTIONS FOR SECOND-ORDER NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATION WITH RANDOM IMPULSES

In this paper, we consider the existence and exponential stability in mean square of mild solutions to second-order neutral stochastic functional differential equations with random impulses in Hilbert space. Firstly, the existence of mild solutions to the equations is proved by using the noncompact measurement strategy and the Mönch fixed point theorem. Then, the mean square exponential stability for the mild solution of the considered equations is obtained by establishing an integral inequality. Finally, an example is given to illustrate our results.

P-Moment Mittag–Leffler Stability of Riemann–Liouville Fractional Differential Equations with Random Impulses

Fractional differential equations with impulses arise in modeling real world phenomena where the state changes instantaneously at some moments. Often, these instantaneous changes occur at random moments. In this situation the theory of Differential equations has to be combined with Probability theory to set up the problem correctly and to study the properties of the solutions. We study the case when the time between two consecutive moments of impulses is exponentially distributed. In connection with the application of the Riemann–Liouville fractional derivative in the equation, we define in an appropriate way both the initial condition and the impulsive conditions. We consider the case when the lower limit of the Riemann–Liouville fractional derivative is fixed at the initial time. We define the so called p-moment Mittag–Leffler stability in time of the model. In the case of integer order derivative the introduced type of stability reduces to the p–moment exponential stability. Sufficient conditions for p–moment Mittag–Leffler stability in time are obtained. The argument is based on Lyapunov functions with the help of the defined fractional Dini derivative. The main contributions of the suggested model is connected with the implementation of impulses occurring at random times and the application of the Riemann–Liouville fractional derivative of order between 0 and 1. For this model the p-moment Mittag–Leffler stability in time of the model is defined and studied by Lyapunov functions once one defines in an appropriate way their Dini fractional derivative.

Compound fault identification of rolling element bearing based on adaptive resonant frequency band extraction

The high frequency resonance (HFR) technique is regarded as a powerful tool for fault diagnosis of rolling element bearings. Different from the usage of the HFR in single fault, the determination of multiple resonant frequency bands under the compound faults and extraneous random impulses is still a challenging task. This paper develops a novel compound fault identification method based on adaptive resonant frequency band extraction. The improved redundant second generation wavelet packet transform is first presented to decompose vibration signal into various narrow bands for providing a fine separation of fault signatures. Then the squared envelope spectrum sparsity criteria is designed to quantify fault characteristics buried in narrow frequency bands. Consequently, the squared envelope spectrum sparsogram is constructed to highlight optimal resonant bands, and the compound faults can be well detected by band-pass filtering and envelope analysis. The numerical and experimental results confirm effectiveness and superiority of the proposed method, which is more sensitive to fault-related impulses and robust to extraneous interferences.

Stability of Boolean networks with state-dependent random impulses

We investigate the stability of Boolean networks (BNs) with impulses triggered by both states and random factors. A hybrid index model is used to describe impulsive BNs. First, several necessary and sufficient conditions for forward completeness are obtained. Second, based on the stability criterion of probabilistic BNs and the forward completeness criterion, the necessary and sufficient conditions for the finite-time stability with probability one and the asymptotical stability in distribution are presented. The relationship between these two kinds of stability is discussed. Last, examples and time-domain simulations are provided to illustrate the obtained results.

Coexistence of Random Subharmonic Solutions of Random Impulsive Differential Equations and Inclusions on a Circle

The coexistence of random periodic solutions with various periods (i.e. subharmonics) is proved to random differential equations on a circle with random impulses of all integer orders. One of the theorems is also extended to random differential inclusions on a circle with multivalued deterministic impulses. These results can be roughly characterized as a further application of the randomized Sharkovsky type theorems to random impulsive differential equations and inclusions on a circle.

On stability of stochastic differential equations with random impulses driven by Poisson jumps

In this article, we study the existence of solutions and their stability of random impulsive stochastic functional differential equations (ISFDEs) driven by Poisson jumps with finite delays. Initially, we prove the existence of the mild solutions to the equations by using Banach fixed point theorem. Then, we study the stability of random ISFDEs through the continuous dependence of solutions on initial condition. Next, we investigate the Hyers Ulam stability results under the Lipschitz condition on a bounded and closed interval. Finally, an example is presented to illustrate our results.

Transient temperature distribution and thermal stresses in a thick plate subjected to random pulses

This paper deals with the determination of second-order statistics (the mean of each component and correlations between components) of the quasi-static temperature distribution and thermal stresses on a thick plate under thermal load. The heated thick circular plate with random internal heat generation acting at random instants of time, in addition to sectional heat supply in the form of random impulses on the upper face, while the lower face is kept at zero temperature, and the fixed circular edge thermally insulated in considered for investigation. A type of Laplace transform method is employed to obtain the analytical solutions for the temperature and stresses statistics. Numerical results demonstrate the effects of the magnitude with the statistics of the temperature and thermal stresses and represented graphically.

Deep Learning Object-Impulse Detection for Enhancing Leakage Detection of a Boiler Tube Using Acoustic Emission Signal

Advances in technology have enhanced the ability to detect leakages in boiler tube components in thermal power plants. As a specific issue, the interaction between the coal fuel stream and the boiler tube membrane generates random and high-amplitude impulses, which negatively affect the measured acoustic emission (AE) signal from leakages. It is essential to detect and practically handle these kinds of impulses. Based on the object detection concept, this paper proposes an impulse detection methodology that employs deep learning flexible boundary regression (DLFBR). First, the shape extraction (SE) preprocessing technique is implemented to yield the shape signal, which contains intrinsic information about the impulse from the raw AE signal. Then, DLFBR extracts and generates both the feature map and the confidence mask from the shape signal to regress a boundary box, which specifies the position of the impulse. For illustration purposes, the proposed algorithm is applied to an experimental leakage detection dataset recorded from a subcritical boiler unit with a tube membrane. Experimental results show that the proposed method is effective for detecting impulses of leakage in a boiler tube testbed, providing 99.8% average classification accuracy.

Exponential Stability Results on Random and Fixed Time Impulsive Differential Systems with Infinite Delay

In this paper, we investigated the stability criteria like an exponential and weakly exponential stable for random impulsive infinite delay differential systems (RIIDDS). Furthermore, we proved some extended exponential and weakly exponential stability results for RIIDDS by using the Lyapunov function and Razumikhin technique. Unlike other studies, we show that the stability behavior of the random time impulses is faster than the fixed time impulses. Finally, two examples were studied for comparative results of fixed and random time impulses it shows by simulation.

A novel blind deconvolution method and its application to fault identification

Blind deconvolution is a method for enhancing the fault feature of rolling element bearings. Based on different maximization criteria, including kurtosis, correlated kurtosis, D-norm, multi-D-norm, and cyclostationarity indicator, different blind deconvolution algorithms have been proposed as powerful tools for fault feature extraction. However, kurtosis and D-norm are susceptible to extreme values, while the other three criteria strongly rely on prior knowledge of the fault period. To overcome the shortcomings of the existing criteria, this study proposes a new criterion called impulse-norm. It is a time-domain parameter defined as the ratio of the average amplitude of the first several maximum energy points to the energy of the entire signal. As opposed to kurtosis and D-norm, the impulse-norm is not affected by strong random impulses. Unlike correlation kurtosis, multi-D-norm and cyclostationarity indicator, it is also independent from the fault period. Based on impulse-norm, we also propose a new deconvolution algorithm called particle swarm optimization-based maximum impulse-norm deconvolution. This blind deconvolution algorithm employs generalized sphere coordinate transformation and adopts the PSO algorithm to optimally solve the filter coefficients by maximizing the impulse-norm of the signal being filtered. The proposed method was validated using simulated signals and high-speed train axle-box bearing experimental signals. The simulation and experimental results indicated that the proposed PSO-MIND method can effectively identify the weak impulse fault feature of rolling element bearings.

Periodicity-Impulsiveness Spectrum Based on Singular Value Negentropy and Its Application for Identification of Optimal Frequency Band

Bearing faults are the main contributors to the failure of motors. Periodic harmonic components from the motor rotating and random impulses caused by the electromagnetic interference heavily trouble vibration-based resonance demodulation techniques. This paper presents a method that accurately identifies the optimal frequency band even with complicated interferences from the motor and industrial field. Singular value negentropy (SVN) is originally applied to measure the periodicity of signal without prior knowledge. Based on the SVN, periodicity-impulsiveness spectrum (PIS) that simultaneously takes periodicity and impulsiveness of fault impulses into consideration is constructed. Guided by the period-oriented kurtosis selection criterion, the resonance frequency band excited by the motor bearing fault is located. The proposed method was validated by the simulated motor bearing signal and the real datasets. Compared with the most popular resonance demodulation methods, kurtogram and protrugram, the proposed method is undoubtedly an alternative method for the identification of optimal resonance band.

Fault Diagnosis of Rolling Bearings Based on Improved Kurtogram in Varying Speed Conditions

Envelope analysis is a widely used method in fault diagnoses of rolling bearings. An optimal narrowband chosen for the envelope demodulation is critical to obtain high detection accuracy. To select the narrowband, the fast kurtogram (FK), which computes the kurtosis of a set of filtered signals, is introduced to detect cyclic transients in a signal, and the zone with the maximum kurtosis is the optimal frequency band. However, the kurtosis value is affected by rotating frequencies and is sensitive to large random impulses which normally occur in industrial applications. These factors weaken the performance of the FK for extracting weak fault features. To overcome these limitations, a novel feature named Order Spectrum Correlated Kurtosis (OSCK) is proposed, replacing the kurtosis index in the FK, to construct an improved kurtogram called Fast Order Spectrum Correlated Kurtogram (FOSCK). A band-pass filter is used to extract the optimal frequency band signal corresponding to the maximum OSCK. The envelope of the filtered signal is calculated using the Hilbert transform, and a low-pass filter is employed to eliminate the trend terms of the envelope. Then, the non-stationary filtered envelope is converted in the time domain into the stationary envelope in the angular domain via Computed Order Tracking (COT) to remove the effects of the speed fluctuation. The order structure of the angular domain envelope signal can then be used to determine the type of fault by identifying its characteristic order. This method offers several merits, such as fine order spectrum resolution and robustness to both random shock and heavy noise. Additionally, it can accurately locate the bearing fault resonance band within a relatively large speed fluctuation. The effectiveness of the proposed method is verified by a number of simulations and experimental bearing fault signals. The results are compared with several existing methods; the proposed method outperforms others in accurate bearing fault feature extraction under varying speed conditions.

Particle swarm optimization algorithm to solve the deconvolution problem for rolling element bearing fault diagnosis

Extraction of the fault related impulses from the raw vibration signal is important for rolling element bearing fault diagnosis. Deconvolution techniques, such as minimum entropy deconvolution (MED), MED adjusted (MEDA) and maximum correlated kurtosis deconvolution (MCKD), optimal MED adjusted (OMEDA) and multipoint optimal MED adjusted (MOMEDA), are typical techniques for enhancing the impulse-like component in the fault signal. This paper introduces the particle swarm optimization (PSO) algorithm to solve the filter of deconvolution problem. The proposed approaches solve the filter coefficients of the deconvolution problems by the PSO algorithm, assisted by a generalized spherical coordinate transformation. Compared with MED, MEDA, and OMEDA, the proposed PSO-MED and PSO-OMEDA can effectively overcome the influence of large random impulses and tend to deconvolve a series of periodic impulses rather than a signal impulse. Compared with MCKD and MOMEDA, the proposed PSO-MCKD and PSO-MOMEDA can achieve good performances even when the fault period is inaccurate. The effectiveness of the proposed methods is validated by the simulated signals. The study of experimental bearing fault signal shows that the PSO based deconvolution methods delivered better performance for rolling element bearing fault detection than the traditional deconvolution methods. Additionally, the proposed methods are compared with the following two popular signal processing methods: the ensemble empirical mode decomposition (EEMD) and fast kurtogram, which are used to highlight the improved performance of the proposed methods.

Operational Modal Analysis of the Laboratory Steel Truss Structure

Abstract Modal analysis in operational conditions is popular way for obtaining natural modes of civil structures such as bridges or dams nowadays. This approach called Operational Modal Analysis (OMA) overcomes difficulties with input forces used for excitation of the structure in Experimental Modal Analysis (EMA). In OMA the input forces are assumed to be stochastic. The paper presents the experimental measurement and analysis of the mode shapes and frequencies of the laboratory steel truss structure using output-only method based on Frequency Domain Decomposition (FDD). FDD technique for a decomposition of the spectral density function matrix in combination with a method for merging measured data from multiple measurement set-ups are both implemented into a data processing tool designed in LabVIEW. Modal exciter and random impulses in random points are used for the structure excitation. The results demonstrate the influence of different types of operational loading on identified modes.

Quantitative diagnosis for bearing faults by improving ensemble empirical mode decomposition

In the bearing health assessment issues, using the adaptive nonstationary vibration signal processing methods in the time-frequency domain, lead to improving of early fault detection. On the other hand, the noise and random impulses which contaminates the input data, are a major challenge in extracting fault-related features. The main goal of this paper is to improve the Ensemble Empirical mode decomposition (EEMD) algorithm and combine it with a new proposed denoising process and the higher order spectra to increase the accuracy and speed of the fault severity and type detection. The main approach is to use statistical features without using any dimension reduction and data training. To eliminate unrelated components from faulty condition, the best combination of denoising parameters based on the wavelet transform, is determined by a proposed performance index. In order to enhance the efficiency of the EEMD algorithm, a systematic method is presented to determine the proper amplitude of the additive noise and the Intrinsic Mode Functions (IMFs) selection scheme. The fault occurrence detection and the fault severity level identification are performed by the Fault Severity Index (FSI) definition based on the energy level of the Combined Fault-Sensitive IMF (CFSIMF) envelope using the central limit theorem. Also, taking the advantages of a bispectrum analysis of CFSIMF envelope, fault type recognition can be achieved by Fault Type Index (FTI) quantification. Finally, the proposed method is validated using experimental data set from two different test rigs. Also, the role of the optimum denoising process and the algorithm of systematic selection of the EEMD parameters are described regardless of its type and estimating the consistent degradation pattern.

Stability Analysis of Cohen–Grossberg Neural Networks with Random Impulses

The Cohen and Grossberg neural networks model is studied in the case when the neurons are subject to a certain impulsive state displacement at random exponentially-distributed moments. These types of impulses significantly change the behavior of the solutions from a deterministic one to a stochastic process. We examine the stability of the equilibrium of the model. Some sufficient conditions for the mean-square exponential stability and mean exponential stability of the equilibrium of general neural networks are obtained in the case of the time-varying potential (or voltage) of the cells, with time-dependent amplification functions and behaved functions, as well as time-varying strengths of connectivity between cells and variable external bias or input from outside the network to the units. These sufficient conditions are explicitly expressed in terms of the parameters of the system, and hence, they are easily verifiable. The theory relies on a modification of the direct Lyapunov method. We illustrate our theory on a particular nonlinear neural network.