Random Impulses Research Articles

Engineering error correcting dynamics in nanomechanical systems

Nanomechanical oscillators are an alternative platform for computation in harsh environments. However, external perturbations arising from such environments may hinder information processing by introducing errors into the computing system. Here, we simulate the dynamics of three coupled Duffing oscillators whose multiple equilibrium states can be used for information processing and storage. Our analysis reveals that, within experimentally relevant parameters, error correcting dynamics can emerge, wherein the system’s state is robust against random external impulses. We find that oscillators in this configuration have several surprising and attractive features, including dynamic isolation of resonators exposed to extreme impulses and the ability to correct simultaneous errors.

Optimal control of stochastic differential equations with random impulses and the Hamilton–Jacobi–Bellman equation

AbstractIn this article, we study the optimal control of stochastic differential equations with random impulses. We optimize the performance index and add the influence of random impulses to the performance index with a random compensation function. Using the idea of stochastic analysis and dynamic programming principle, a new Hamilton–Jacobi–Bellman (HJB) equation is obtained, and the existence and uniqueness of its viscosity solution are proved.

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.

Existence and Hyers–Ulam Stability for Random Impulsive Stochastic Pantograph Equations with the Caputo Fractional Derivative

In this paper, we study the existence, uniqueness and Hyers–Ulam stability of a class of fractional stochastic pantograph equations with random impulses. Firstly, we establish sufficient conditions to ensure the existence of solutions for the considered equations by applying Schaefer’s fixed point theorem under relaxed linear growth conditions. Secondly, we prove the solution for the considered equations is Hyers–Ulam stable via Gronwall’s inequality. Moreover, the previous literature will be significantly generalized in our paper. Finally, an example is given to explain the efficiency of the obtained results.

State-Feedback Set Stabilization of Boolean Networks With State-Dependent Random Impulses.

In this article, we are devoted to addressing the state-feedback set stabilization of Boolean control networks with state-dependent random impulses by utilizing a hybrid index model. By comparison with the previous impulsive Boolean networks, this model can be used to describe the instantaneousness of various impulsive behaviors more clearly. In order to avoid the occurrence of Zeno phenomenon, we first introduce the basic concept of forward completeness and further establish the judging criterion. After that, an algorithm is presented to derive the largest control invariant subset of a given subset. Based on this, we derive a necessary and sufficient criterion for finite-time feedback set stabilizability. Similarly, the result is also obtained for the asymptotic case, and the asymptotic set stabilizers are designed by dividing the whole state space into several layers. Moreover, we also investigate the relationships between different stabilizabilities. Last, two illustrative examples are presented to demonstrate the efficiency of the theoretical results.

Hamilton‐Jacobi‐Bellman equation based on fractional random impulses system

AbstractIn this talk, we consider the optimal control problem for fractional order random impulses differential equations (), and there is no corresponding Hamilton‐Jacobi‐Bellman (HJB) equation proposed for fractional order differential equations in existing literature. The lack of semi group properties in fractional order makes the original dynamic programming methods unable to directly handle fractional order problems. We have dealt with this problem by combining the properties of fractional order integrals. In solving this problem, we found that the order of the original system in HJB equation is at least 1. When the order is less than 1, our approach to fractional order ideas provides a possibility to solve the problem.

Vibration-based identification of lubrication starved bearing using spectral centroid indicator combined with minimum entropy deconvolution

For bearings under starved lubrication conditions, direct contacts occur between metallic surfaces, leading to random impulses in vibration response. This paper proposes a vibration-based scheme for starved lubrication identification. Minimum entropy deconvolution (MED) is utilized to enhance the weak random impulses caused by lubricant starvation. Moreover, a starved lubrication feature (SLF) based on the spectral centroid indicator is constructed to diagnose starved lubrication. The efficacy is verified by a comparative study conducted on a bearing test bench. Bearing vibration signals under two lubrication conditions are collected at different rotating speeds. The kurtosis of raw signals under starved lubrication is less than 4, but increases to above 7 after MED. For evaluation of lubrication conditions classification, the Davies-Bouldin index (DBI) of SLF is 0.042, significantly better than that of traditional characteristics (RMS DBI = 0.484, kurtosis DBI = 0.559). The results indicate that the SLF can identify starved lubrication conditions under different speeds.

Approximate controllability of second-order neutral stochastic differential evolution systems with random impulsive effect and state-dependent delay

<p>In this paper, we have discussed a class of second-order neutral stochastic differential evolution systems, based on the Wiener process, with random impulses and state-dependent delay. The system is an extension of impulsive stochastic differential equations, since its random effect is not only from stochastic disturbances but also from the random sequence of the impulse occurrence time. By using the cosine operator semigroup theory, stochastic analysis theorem, and the measure of noncompactness, the existence of solutions was obtained. Then, giving appropriate assumptions, the approximate controllability of the considered system was inferred. Finally, two examples were given to illustrate the effectiveness of our work.</p>

Dynamic Output Quantized Control for Linear Delayed Systems With Random Impulses

Dynamic Output Quantized Control for Linear Delayed Systems With Random Impulses

ANALYSIS OF GLOBAL EXPONENTIAL STABILITY FOR NONLINEAR IMPULSIVE STOCHASTIC SYSTEMS WITH DELAY USING REGULARIZATION TECHNIQUES

The W-transform in the form of the regularization techniques, based on inverse-positive matrices, is used to obtain verifiable global stability conditions for linear and nonlinear stochastic delay systems with random coefficients and impulses at random times. The results are conveniently formulated in terms of coefficients of the systems. Several examples illustrating the main results are offered.

THEORETICAL MODELS OF CHARGE TRANSFER PROCESSES IN NONPOLAR MEDIA

The charge transfer processes in nonpolar media are considered in the work. The nonpolar medium is regarded as a field of random forces or impulses, and this field acts on the reacting particles. The interaction of reagents with the medium is described through the function of fluctuation of the impulse of a particle of the medium with the speed of the reagent particle. When calculating the kinetic parameters of such a system, the quantum theory of charge transfer processes was used using Green's functions of the impulse density operators of the condensed medium. Analytical expressions for the kinetic parameters of the process are obtained.

An alternative bearing fault detection strategy for vibrating screen bearings

The transformation of the mining machinery industry is oriented towards the adoption of highly sophisticated technologies, with the aim of enhancing operational efficiency. Specifically, there is a focus on improving the nature and quality of operations carried out, such as vibrating screen. Vibrating screens, being one of the pivotal machines, have gained extensive utilization in mining processing plants. However, the demanding working conditions can lead to potential failures in certain components of vibrating screens. Bearings are one of the components that are susceptible to faults. Moreover, owing to the unique working environment and structure of vibrating screens, the signals extracted from defective bearings in vibrating screens exhibit greater complexity and distinctiveness, including (i) vibration interference related to the unbalanced shafts, (ii) cyclic impulses produced by the damaged bearing, (iii) non-cyclic random impulsive noise owing to pieces of coal falling into the deck, and (iv) inevitable noise from environmental conditions. To address this issue, an alternative procedure for bearing fault detection from vibrating screens served in the coal industry is proposed in the work. The strategy for bearing fault signature extraction covers three main steps: (a) a new fast resampled iterative filtering (FRIF) method is utilized to remove the vibration interference produced by the unbalanced shafts and simultaneously eliminate large amounts of background noise; (b) a signal processing method based stable distribution is designed to cancel the random impulses (impulsive noise); and (c) an improved energy operator demodulation technique is proposed to identify the bearing fault characteristics from the purified signal. The proposed strategy is validated using simulated and real tests.

Stability and guaranteed cost control for linear impulsive systems with random impulses: Application to stochastic event‐triggered control

SummaryThis paper proposes a systematic framework for stability and guaranteed cost control of linear impulsive systems subject to random time‐ and event‐triggering impulses. Moment stability criteria and design methods of time‐ and event‐triggered controllers with guaranteed quadratic performance for the impulsive system are established. It shows that the proposed event‐triggered controller in the sense that it guarantees at least the same quadratic performance function bound as the designed time‐triggered guaranteed cost controller, however, with a larger, or at most equal, average inter‐transmission time. Based on the proposed framework of random‐impulses systems, a stochastic dynamic event‐triggered control strategy is proposed to solve sampled‐data control systems in the presents of sporadic measurements or stochastic sampling. Numerical simulations illustrate the effectiveness of the proposed theoretical results.

Periodicity-assist double delay-controlled stochastic resonance for the fault detection of bearings

This paper analyses the stochastic resonance of a double delay-controlled nonlinear system based on the high-order-degradation potential function. It provides a theoretical derivation of the stationary probability density, mean first-passage time (MFPT), and signal-to-noise ratio (SNR), while the marginal probability density is examined via Monte-Carlo simulation. In the field of fault detection for faulty bearings, the stochastic resonance of the nonlinear system encounters a challenge where the exact fault period must be known beforehand. Unfortunately, it is not available for the real engineering application. Consequently, this paper proposes the periodicity-assisted stochastic resonance method, which uses the blind deconvolution technique. The proposed method allows for adaptive determination of the fault frequency from the vibration signal and successfully enhances the power of the signal component corresponding to the determined fault frequency. Compared with the state-of-the-art methods, the proposed method shows better performance, which is validated by the simulated and experimental data. Overall, the proposed method is advantageous for enhancing the weak fault characteristic which is interfered by the strong noise and random impulses.

Dynamic Event-Triggered Control of Continuous-Time Systems With Random Impulses

Dynamic Event-Triggered Control of Continuous-Time Systems With Random Impulses

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.

Electricity consumption simulation using random coefficient periodic autoregressive model

The concept of a continuous-time conditional linear random process involves a random kernel being integrated stochastically by a process with independent increments, which is often called a “generative process”. In cases where the “generative process” is Poisson, the resulting model represents an investigated signal as a sum of numerous stochastically dependent random impulses each of which occurs according to some inhomogeneous Poisson arrival process. This model can be applied to represent various processes related to energy consumption, such as electricity loads of electrical power systems, gas and water consumption, and other energy resources, while also considering the signals’ cyclostationarity, which is usually caused by the rhythmic nature of consumer behaviour. A member of the discretetime conditional linear cyclostationary random processes class is the random coefficient periodic autoregressive (RCPAR) model, which is appropriate for use in energy informatics, including estimation, forecasting, and computer simulation purposes. The primary objective of the paper is to establish a procedure for simulating the hourly electricity consumption of small and medium-sized enterprises using the RCPAR model, which has periodic parameters and creates cyclostationary properties while also accounting for the investigated process conditional heteroscedasticity. The statistical estimation step of the proposed procedure uses the general methodology for estimating the parameters of the RCPAR model and the methods of statistical analysis of cyclostationary signals. This step is used to identify the simulation characteristics. The simulation step is based on the methods of cyclostationary white noise generation and its transformation by a digital linear filter with random parameters. The last ones are obtained using the Gaussian random vectors computer simulation methods, taking into account the cyclostaionarity property.

Non-Contact Impact Source Localization in Composite Symmetry Panels Based on A0 Mode of Lamb Waves

Traditional methods for detecting damage in engineering structures often use offline static damage detection. To enable the real-time and precise identification of dynamic damage while maintaining symmetry in engineering structures, this study primarily concentrates on isotropic plate structures widely employed in engineering. Moreover, fiberglass board composite plates were opted as a specific research object. By utilizing the weak S0 mode signals generated by low-frequency ultrasonic Lamb waves, the non-stationary A0 wave signals in the composite symmetry plate structure are collected using the non-contact SLDV (Scanning Laser Doppler Vibrometer) technique. The frequency characteristic parameters in the vibration signals are obtained through HHT (Hilbert–Huang Transform) analysis, followed by filtering and noise reduction. Finally, the circular trajectory intersection method is employed to accurately locate dynamic damage sources in plate structures with different material properties, thereby validating the positioning effect of contact sensors in detecting impacts caused by random impulses.

Finite time stability of time-varying stochastic nonlinear systems with random impulses

ABSTRACT This article studies the finite time stability (FNTS) of time-varying nonlinear stochastic systems with random impulses. We provide sufficient conditions for the FNTS or even fixed time stability (FXTS) for time-varying stochastic systems under two cases: (1) The impulse time is deterministic; (2) The impulse time is random. For case (1), we use the reverse average dwell time to investigate FNTS, but for case (2), we employ the Poisson process theory to solve the stability problem. In addition, the stability criteria capture the stabilising effect of stochastic noise in the FNTS problem. Finally, the correctness of the theoretical results is verified with two numerical examples. As far as the author knows, no one has studied the FNTS of time-varying stochastic systems with random impulses.

Manifold learning-assisted sparse filtering method for machinery fault diagnosis

Sparse filtering (SF) has received considerable attentions in the machinery fault diagnosis thanks to its ability to extract the fault-related features using their sparsity. However, the existing SF methods have dilemmas with the empirical selection of model parameters, the loss of fault-related information caused by a screening way for the target mode, and the singularity of results induced by some large-amplitude random impulses (LARIs). Hence, a manifold learning-assisted SF method is proposed for machinery fault-related feature enhancement in this study. First, an improved intrinsic component filtering (ICF) is presented for extracting the multiple modes with feature enhancement, where the parameters of ICF are adaptively determined by using the optimization object to avoid the empirical selection of parameters. Second, the manifold learning is introduced to compress the enhanced multiple modes to overcome the loss of fault-related information; thus the intrinsic manifolds are obtained for disclosing the buried fault-related features and suppressing the band-in noise. Third, an adaptively weighting strategy for these intrinsic manifolds is constructed to obtain a final representative mode for conducting the machinery fault diagnosis. Meanwhile, the LARIs coupled with intrinsic manifolds are calibrated according to their statistical information to resolve the singularity of the representative features. Simulation and experiments show that the proposed method is more effective in extracting fault-related features than some existing methods.