non-Gaussian Vibration Research Articles

Numerical Simulation and Influence of Non-Gaussian Vibrations on Flexible Robotic Systems

Random vibration excitation is a standard method for obtaining the dynamic properties of aerospace structures and simulating loading conditions. Shaker-based random excitation and traditional finite element analysis techniques use random vibrations, assuming a Gaussian distribution of excitation impulse magnitudes. While Gaussian signals may sufficiently describe some vibrational environments, many real-world excitations have non-Gaussian distributions. These signals may contain vibrational impulses larger than those observed in a Gaussian signal and could cause damage if not considered. This paper examines the influence of non-Gaussian signals on flexible vs. rigid robotic architectures using NASA JPL’s Pop-Up Flat Folding Explorer Robot (PUFFER) and Cooperative Autonomous Distributed Robotic Explorer (CADRE). The results indicate that flexible systems can be significantly impacted by a non-Gaussian excitation profile and that neither a typical enveloping of a Gaussian excitation nor a superposition of the responses to a worst-case impulse load with the response to a Gaussian signal was sufficient to bound the response due to non-Gaussian excitation. The driving mechanism for increased sensitivity of flexible robotic systems appears to be inertial, and designers may consider shifting the relative flexibility of the system or its constraints to force particular deformation modes or designing hinge mechanisms with increased damping to minimize the influence of non-Gaussian signals on the response of a flexible robotic structure.

Research on Numerical Simulation Method of Nonstationary Random Vibration Signal Sensor in Railway Transportation

During railway transportation, due to various factors such as road conditions and operating conditions and produced vibrations and shocks, this kind of vibration environment may cause fatigue damage to on-board equipment and transported goods. The authors propose a research on the numerical simulation method of the nonstationary random vibration signal sensor of railway transportation; first, they establish the mathematical model of the railway nonstationary random vibration signal sensor and then introduce the method of reconstructing the railway nonstationary random vibration signal sensor. For railway nonstationary non-Gaussian random vibration reconstruction signal, compare the time-domain characteristics of the sampled signal, and for railway nonstationary non-Gaussian random vibration reconstruction signal, compare the frequency domain characteristics of the sampled signal. The results show that the relative error of the RMSM function is within 6%, the relative error of the sliding bias function is within 10%, and the relative error of the sliding kurtosis function is within 8%. The energy distribution of the edge Hilbert amplitude spectrum is very similar, with absolute error less than 6%. The energy fluctuations are similar in each band, with absolute error rates less than 4% in most bands. The method proposed in this article, suitable for reconstruction of railway nonstationary Gaussian random vibration and nonstationary non-Gaussian vibration signal sensor, verifies the effectiveness and feasibility of the signal reconstruction method. The model and signal reconstruction method proposed in this paper are applied to the railway nonstationary Gaussian and nonstationary non-Gaussian random vibration sampling signals.

Alternative Measures of Dependence for Cyclic Behaviour Identification in the Signal with Impulsive Noise—Application to the Local Damage Detection

The local damage detection procedures in rotating machinery are based on the analysis of the impulsiveness and/or the periodicity of disturbances corresponding to the failure. Recent findings related to non-Gaussian vibration signals showed some drawbacks of the classical methods. If the signal is noisy and it is strongly non-Gaussian (heavy-tailed), searching for impulsive behvaior is pointless as both informative and non-informative components are transients. The classical dependence measure (autocorrelation) is not suitable for non-Gaussian signals. Thus, there is a need for new methods for hidden periodicity detection. In this paper, an attempt will be made to use alternative measures of dependence used in time series analysis that are less known in the condition monitoring (CM) community. They are proposed as alternatives for the classical autocovariance function used in the cyclostationary analysis. The methodology of the auto-similarity map calculation is presented as well as a procedure for a “quality” or “informativeness” assessment of the map is proposed. In the most complex case, the most resistant to heavy-tailed noise turned out the proposed techniques based on Kendall, Spearman and Quadrant autocorrelations. Whereas in the case of the local fault disturbed by the Gaussian noise, the most efficient proved to be a commonly-known approach based on Pearson autocorrelation. The ideas proposed in the paper are supported by simulation signals and real vibrations from heavy-duty machines.

Vibration Fatigue Damage Estimation by New Stress Correction Based on Kurtosis Control of Random Excitation Loadings.

In the pioneer CAE stage, life assessment is the essential part to make the product meet the life requirement. Commonly, the lives of flexible structures are determined by vibration fatigue which accrues at or close to their natural frequencies. However, existing PSD vibration fatigue damage estimation methods have two prerequisites for use: the behavior of the mechanical system must be linear and the probability density function of the response stresses must follow a Gaussian distribution. Under operating conditions, non-Gaussian signals are often recorded as excitation (usually observed through kurtosis), which will result in non-Gaussian response stresses. A new correction is needed to make the PSD approach available for the non-Gaussian vibration to deal with the inevitable extreme value of high kurtosis. This work aims to solve the vibration fatigue estimation under the non-Gaussian vibration; the key is the probability density function of response stress. This work researches the importance of non-Gaussianity numerically and experimentally. The beam specimens with two notches were used in this research. All excitation stays in the frequency range that only affects the second natural frequency, although their kurtosis is different. The results show that the probability density function of response stress under different kurtoses can be obtained by kurtosis correction based on the PSD approach of the frequency domain.

The detection of non-Gaussian vibration with improved sensing performance in [formula omitted]-OTDR

In structural health monitoring, vibrations often behave as non-Gaussian process, such as gear and engine failure. In this paper, a high-order cumulants algorithm-based phase-sensitive optical time-domain reflectometry is proposed to detect and analyze non-Gaussian vibration. When disturbances with non-Gaussian probability distribution are applied on the sensing fiber, the probability distribution of the Rayleigh backscattering deviates from the standard Gaussian distribution. The 3rd-order cumulant of the Rayleigh backscattering is calculated to extract the non-Gaussian signal from background white noises. Simulations and experiments are carried out. The experimental results indicate that the signal-to-noise ratio is improved by up to ∼14 dB with 1500 m long sensing fiber. Due to the cubic operation of the algorithm, the spatial resolution is further enhanced to 5 m with pulse width of 100 ns.

Kernel Density Estimation Based Gaussian and Non-Gaussian Random Vibration Data Induction for High-Speed Train Equipment

Because general statistics tolerance is not applicable to the induction of non-Gaussian vibration data and the methods for converting non-Gaussian data into Gaussian data are not always effective and can increase the estimation error, a novel kernel density estimation method in which induction is carried out on power spectral density data for the measured vibration of high-speed trains is proposed in this paper. First, data belonging to the same population of power spectral density are merged into the same feature sample. Then, the probability density function of all power spectral density values at the first frequency point is calculated through the kernel density estimation method, and the upper-limit estimate of all power spectral density values under the set quantile is obtained. This process is repeated, and the upper limit values of the power spectral density values at all frequency points can be obtained to convert the measured acceleration data to the acceleration power spectral density spectrum of the vibration test. Engineering examples are used to verify the proposed method. For the same Gaussian power spectral density data, the relative error between the root mean squares of the power spectral density spectrum obtained from induction by the kernel density estimation method and the statistics tolerance is 0.155% ~1.55%; for the non-Gaussian power spectral density data, the acceleration power spectral density spectrum of the non-Gaussian vibration can be obtained with the induction by the kernel density estimation method. The proposed kernel density estimation method satisfies the induction requirements for the measured Gaussian and non-Gaussian vibration data of high-speed trains with two different distributions, and its induction results have very good universality and estimation accuracy.

Multiple-input multiple-output non-stationary non-Gaussian random vibration control by inverse system method

Abstract This paper investigates the control method for multi-input multi-output non-stationary non-Gaussian random vibration test with the specified references composed of stationary power spectra, moving root mean square distributions and moving kurtosis distributions. The objective of random vibration test is to force the response signals of test structure to satisfy the specified references within tolerances. An inverse system method in time domain is used to guarantee the control of response time-frequency characteristics independently and simultaneously. The evolutionary spectrum theory is utilized to establish the matrix representation of non-stationary non-Gaussian input-output relationships of a linear dynamic system in frequency domain. To analyze a non-stationary non-Gaussian vibration signal, two sets of random numbers named moving root mean square and moving kurtosis are used to modulate a stationary random signal. The transformation process theory is utilized to obtain moving root mean square and moving kurtosis by a moving root mean square distribution and a moving kurtosis distribution respectively. The control algorithms are presented to update the drive signals according to the deviations between responses and references. A numerical example by a cantilever beam and a biaxial vibration test are carried out and the results demonstrate the feasibility and validity of the proposed methods.

Experimental Research on Vibration Fatigue of CFRP and Its Influence Factors Based on Vibration Testing

A new research method based on vibration testing for the vibration fatigue of FRP was proposed in this paper. Through the testing on a closed-loop controlled vibration fatigue test system, the vibration fatigue phenomenon of typical carbon-fiber-reinforced plastic (CFRP) cantilevered laminate specimens was carefully studied. Moreover, a method based on the frequency response function was proposed to monitor the fatigue damage accumulation of specimens. On the basis of that, the influence factors that affect the vibration fatigue life of CFRP were experimentally studied. The influence of amplitude probability distribution of the vibration load spectrum on the fatigue life was deeply explored. Compared with Gaussian random vibration, the non-Gaussian random load has a significant impact on the vibration fatigue life of CFRP. The experimental results also showed that the magnitude of power spectral density (PSD) has a significant effect on the vibration fatigue life of specimens. For Gaussian vibration load, the frequency bandwidth almost has no effects on the vibration fatigue life of CFRP. However, for non-Gaussian vibration load, it has a great impact on the fatigue life. When PSD magnitude and frequency bandwidth are constant, the root mean square (RMS) is proportional to the vibration fatigue life of composites.

On the Shaker Simulation of Wind-Induced Non-Gaussian Random Vibration

Gaussian signal is produced by ordinary random vibration controllers to test the products in the laboratory, while the field data is usually non-Gaussian. Two methodologies are presented in this paper for shaker simulation of wind-induced non-Gaussian vibration. The first methodology synthesizes the non-Gaussian signal offline and replicates it on the shaker in the Time Waveform Replication (TWR) mode. A new synthesis method is used to model the non-Gaussian signal as a Gaussian signal multiplied by an amplitude modulation function (AMF). A case study is presented to show that the synthesized non-Gaussian signal has the same power spectral density (PSD), probability density function (PDF), and loading cycle distribution (LCD) as the field data. The second methodology derives a damage equivalent Gaussian signal from the non-Gaussian signal based on the fatigue damage spectrum (FDS) and the extreme response spectrum (ERS) and reproduces it on the shaker in the closed-loop frequency domain control mode. The PSD level and the duration time of the derived Gaussian signal can be manipulated for accelerated testing purpose. A case study is presented to show that the derived PSD matches the damage potential of the non-Gaussian environment for both fatigue and peak response.

Experimental Design and Validation of an Accelerated Random Vibration Fatigue Testing Methodology

Novel accelerated random vibration fatigue test methodology and strategy are proposed, which can generate a design of the experimental test plan significantly reducing the test time and the sample size. Based on theoretical analysis and fatigue damage model, several groups of random vibration fatigue tests were designed and conducted with the aim of investigating effects of both Gaussian and non-Gaussian random excitation on the vibration fatigue. First, stress responses at a weak point of a notched specimen structure were measured under different base random excitations. According to the measured stress responses, the structural fatigue lives corresponding to the different vibrational excitations were predicted by using the WAFO simulation technique. Second, a couple of destructive vibration fatigue tests were carried out to validate the accuracy of the WAFO fatigue life prediction method. After applying the proposed experimental and numerical simulation methods, various factors that affect the vibration fatigue life of structures were systematically studied, including root mean squares of acceleration, power spectral density, power spectral bandwidth, and kurtosis. The feasibility of WAFO for non-Gaussian vibration fatigue life prediction and the use of non-Gaussian vibration excitation for accelerated fatigue testing were experimentally verified.

The Simulation of Non-Gaussian Vibration Environment on Railway

During the transportation of railway, all kinds of transportation equipment are subject to random vibration generated by random road excitation. In practice, however, a lot of vibration caused by poor environment of railway show non-Gaussian incentive features. Based on IFFT transformation-based of Gaussian random, by analyzing the relationship among phase angle, kurtosis and skewness, the paper uses the second phase modulation method to generate the non-Gaussian excitation signal with the measured vibration data in the process of train running, and then using MATLAB, this method will simulate the real railway vibration of non-Gaussian excitation signal. The simulation result provides the theory basis for the reliability verification of laboratory and shipping goods, and has a certain practical significance for the improvement of train operation safety.

Fault detection in non-Gaussian vibration systems using dynamic statistical-based approaches

This article develops and contrasts two different statistical-based techniques for monitoring mechanical systems that produce stochastic, non-Gaussian, and correlated vibration signals. Existing work in this area relies on the assumption that the recorded signals follow a multinormal distribution and/or the data model is static, i.e. the signals are assumed to possess no serial correlation. The developed approaches rely on (i) recent work on independent component analysis and support vector data description that is applied to a dynamic data structure and (ii) the incorporation of the statistical local approach into a dynamic data representation. The analysis of experimental data from a gearbox system confirms (i) significant auto- and cross-correlation within and among these signals and (ii) that they cannot be assumed to follow Gaussian distributions. The application of both approaches showed that they are more sensitive to incipient faults than conventional multivariate statistical methods.

Temperature dependence of the dynamics of methylene chains in aliphatic nylons of different chain length

Temperature-dependent inelastic neutron backscattering experiments with μ eV energy resolution on nylons of different chain length show the onset of dynamic processes on the time scale of 10 −8 s far below T g, around 200 K. The evaluation in terms of non-Gaussian vibrations reveals an apparent mean square displacement which increases with the chain length. It is similar for nylon 6, 46 and 66, but shows lower values for nylon 3 and much larger mean square displacements for nylon 12.