non-Gaussian Random Vibration Research Articles

Modified time domain randomization technique for multi-shaker non-stationary non-Gaussian random vibration control

Traditional random vibration environmental tests simulate stationary Gaussian random vibration environments. In this work, the generation and closed-loop control of multi-shaker non-stationary non-Gaussian random vibration signals with the modified time domain randomization technique are studied. The amplitude modulation function is introduced to control the non-stationary and non-Gaussian characteristics that the root mean square value of the generated signal changes with time. The kurtosis relationship between the one frame pseudo-random signal and consecutive true random signal is derived theoretically. It is found that the kurtosis of the consecutive non-stationary random signal is determined by the amplitude modulation function and kurtosis of the pseudo-random signal. The standard deviation of the time-varying root mean square reflects the non-stationary characteristics of the generated signal. A control strategy for multi-shaker non-stationary non-Gaussian random vibration environmental test is proposed. The non-stationary and non-Gaussian characteristics are extracted from the measured response signals so that the power spectral densities, kurtoses and non-stationary characteristics can be controlled simultaneously. The results from the simulation examples and multi-shaker vibration experiments prove the feasibility and practicability of the proposed non-stationary non-Gaussian random signal generation method and control strategy.

Prototyping of vibration testing machine that is generated non-gaussian random vibration which is determined by probability density function and power spectrum

Prototyping of vibration testing machine that is generated non-gaussian random vibration which is determined by probability density function and power spectrum

Prototyping of vibration testing machine that is generated non-gaussian random vibration which is determined by probability density function and power spectrum

Prototyping of vibration testing machine that is generated non-gaussian random vibration which is determined by probability density function and power spectrum

Non-stationary non-Gaussian random vibration analysis of Duffing systems based on explicit time-domain method

Non-stationary non-Gaussian random vibration problems of structures are challenging and drawing increasing attention. In the present study, firstly, an explicit time-domain method (ETDM) is proposed to determine the higher-order response statistics of linear systems subjected to non-stationary non-Gaussian random excitations, in which the first four orders of cumulants of dynamic responses are directly formulated through the cumulant operation rule based on the explicit expressions of responses. Secondly, an equivalent linearization – explicit time-domain method (EL-ETDM) is further developed to solve the non-stationary non-Gaussian random vibration problems of Duffing systems, in which the equivalent linear system is derived discarding the assumption of Gaussian response, and the corresponding higher-order cumulant analyses of the linearized system are accomplished by the efficient ETDM. The present approach can account for non-Gaussian random excitations with arbitrary forms, and two specific applications to the Poisson white noise and the square form of Gaussian random process are investigated. Four numerical examples are presented to demonstrate the effectiveness of the proposed methods.

Investigation of planar translational and rotational stationary non-Gaussian random vibration test

Multi-shaker random vibration control with coordinate transformation technique is an advanced mechanical environment test method that translational and rotational vibrations of structure can be controlled simultaneously. This work presents theoretical and experimental investigations of multi-shaker planar translational and rotational non-Gaussian random vibration tests. First, the coordinate transformation technique is used to obtain the translational and rotational vibration responses of the test structure. Then the control procedure is formulated theoretically with matrix presentation in which a new nonlinear transformation method for generating non-Gaussian random signals is proposed. The correlation between translational and rotational vibrations is explored briefly from the perspective of common square control and transformation control. The influence of elastic characteristics of the test structure on the response spectral densities is investigated and a level definition method for translational and rotational vibrations is proposed. Finally, a planar translational and rotational non-Gaussian random vibration test is carried out to verify the validity of the proposed methods.

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.

Power spectrum and kurtosis separation method for multi-shaker non-Gaussian random vibration control

An innovative power spectrum and kurtosis separation control strategy for a non-Gaussian random vibration test is proposed in this work. In the existing non-Gaussian random vibration test method, the spectrum and kurtosis control channels are identical and the responses of non-control channels usually approach Gaussian. This work aims at the practical situation where the spectrum and kurtosis control channels are not completely coincident. The key ideas of the proposed non-Gaussian separation control strategy are that the predefined reference spectral densities of the spectrum control channels are used to generate equivalent reference spectral densities of the kurtosis control channels, then the equivalent reference spectral densities combined with the reference kurtoses are used to obtain the desired drive signals. For the single-shaker separation control, the non-Gaussian separation control method can be implemented. When it comes to the multi-shaker case, the coupling problems caused by the cross spectra and inherent multi-input multi-output physical system have an influence on the setting between the reference spectra and reference kurtoses and on the simultaneous control of the response spectra and response kurtoses. Simulation examples with a mass-spring-damping system are carried out and the results are discussed. Finally, biaxial separation and non-separation non-Gaussian random vibration tests are provided to verify the feasibility of the proposed control method.

Continuous convolution and nonlinear transformation for multi-shaker non-Gaussian random vibration control

This study proposes a continuous convolution method combined with memoryless nonlinear transformation for multi-input multi-output stationary non-Gaussian random vibration tests. The challenge of the multi-shaker non-Gaussian random vibration test lies in the coupling problems that are manifested in the inherent physical system and in the existence of cross-spectral densities. In the presented method, the independent stationary Gaussian random signals pass through a designed finite impulse response filter with a convolution manipulation first, and then the resulting signals are transformed to the non-Gaussian random signals by the memoryless nonlinear transformation method. The desired drive signals are obtained by the input–output relationship in the frequency domain. The finite impulse response filter is constructed by the frequency sampling technique in which the amplitude characteristics of the filter are determined by the predefined reference power spectral densities. A new monotonic nonlinear transformation function with an approximate kurtosis solution is provided. It only contains one parameter for kurtosis control both in sub-Gaussian and super-Gaussian cases. The memoryless nonlinear transformation is used to maintain the cross-spectral densities, although some distortions are introduced to the power spectra during the transformation process. The inverse system method is used to overcome the coupling problem caused by the inherent physical system. A simulation example and a triaxial vibration test are carried out, and the results indicate the validity and feasibility of the proposed method.

Analysis of low damping ratios in multi-exciter stationary non-Gaussian random vibration control

This article investigates the influence of low damping ratios on the performance of the multi-exciter stationary non-Gaussian random vibration control system. The basic theory of the multi-exciter stationary non-Gaussian random vibration method is reviewed first, and then the influences of low damping ratios on multi-output spectra and kurtoses are analyzed. The low damping ratios cause an ill-conditioned problem which will make the drive spectral matrix solution inaccurate; thus, some spectral lines located at resonance peaks in the response spectra cannot be modified within the preset tolerances by the control algorithms. The regularization method is used to alleviate the calculation error. The output kurtoses are dependent not only on the characteristics of the system but also on the input signals. It is found that the kurtosis control will be intractable if the damping ratios are very low. A two-input two-output cantilever beam simulation example is described to illustrate the analysis results.

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.

Characterizing non-Gaussian vibration loading using the trispectrum

This paper addresses the use of higher-order spectra to study the non-Gaussian nature of random vibration loading. Since the power spectral density is only a full description for stationary Gaussian processes, specifying non-Gaussian random vibration loading requires a sophisticated statistical description. In recent research higher-order statistical moments such as skewness and kurtosis have been used to define non-Gaussian properties of vibration loading. However, useful information contained in the spectral representation of these moments is neglected. This paper introduces the trispectrum as a tool for analyzing vibration loading. It is the spectral representation of the fourth-order moment and thus extends the information content of the kurtosis. For demonstration several common methods for generating non-Gaussian loading are reviewed and used to derive loads that reproduce the power spectral density and kurtosis of a real in-service loading. These loads are analyzed using Fatigue Damage Spectra and trispectra to relate structural response behavior to their non-Gaussian nature. The results suggest that the trispectrum is a valuable tool for analyzing and classifying non-Gaussian random loading.

Fatigue life due to non-Gaussian excitation – An analysis of the Fatigue Damage Spectrum using Higher Order Spectra

The fatigue damage spectrum (FDS) is an established tool for the assessment of the fatigue damage potential of any kind of vibration loading exerted on vibratory structures. It is especially useful for describing the fatigue damage potential of non-Gaussian random vibration signals, because for this type of signal no comprehensive, theoretically based statistical description is available. As the current definition of the FDS is based on the assumption of single degree of freedom vibration systems, the presented work analyses the resulting limitations for general vibration systems with multiple resonant frequencies. Improvements based on findings from higher-order spectra are proposed.

Generation of sine on random vibrations for multi-axial fatigue tests

Abstract This paper deals with the generation of multi-axial sine on random mixed vibration environments with specified references. Unlike pure vibration environments such as sine or random excitation, the difficulties of the superposition of sine on random vibration control lie in the separation of mixed vibration signals and simultaneous control of sine and random components. An improved correlation integral method is proposed to separate the mixed vibration signals. Considering the non-Gaussian random vibration characteristics, the control references of random component are comprised of multi-output response skewnesses, kurtoses, auto-power spectral densities, phase and coherence coefficients. The Hermite polynomial model transformation method is introduced to transform stationary Gaussian random signals to stationary non-Gaussian random signals with specified skewnesses and kurtoses. The control references of sine component consist of multi-output response amplitudes and phase differences. Closed loop control algorithms are presented to update the drive signals according to the deviations between responses and references. And finally, the results from a tri-axial sine on random mixed vibration control test show the feasibility and efficiency of the proposed methods.

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.

Based on the virtual experiment study of the impact of load sequence on the calculation process of random vibration fatigue damage.

At present, the linear fatigue accumulation theory proposed by Miner is used to calculate the fatigue problem of random vibration. In this process, the loading order of the loads is ignored, so that the results obtained are riskier. The nonlinear fatigue cumulative damage theory takes into account the effects of the load loading sequence, but the calculation becomes more complicated. Many scholars have shown that the fatigue calculation of alternating loads is not strictly linear, and the high and low order will affect the damage index. This phenomenon will be more obvious in the random vibration process. In this paper, the effects of loading sequence on the calculation of non-Gaussian random vibration fatigue damage are studied by virtual experiments. Through the phase selection method, 7 sets of excitations with different kurtosis were loaded onto the notched specimen. Through the calculation results of fatigue damage in the notch sensitive area, it was confirmed that the damage calculated by linear and nonlinear cumulative damage formula was improved with the increase of kurtosis. The results can make a significant difference.

Multi-exciter stationary non-Gaussian random vibration test with time domain randomization

Abstract This paper presents a new control method for multi-input multi-output stationary non-Gaussian random vibration test using time domain randomization. The control objectives are composed of response skewnesses, kurtoses and power spectral densities. The generation process of stationary and coupled reference non-Gaussian signals by specified reference skewnesses, kurtoses and spectra is analyzed. The reference non-Gaussian signals combined with system frequency response functions are then utilized to obtain the desired drive signals for dynamic inputs, in which the inverse system method in the frequency domain is employed. The primary advantages of the proposed methods are the high computational efficiency and simultaneous control of the time-frequency characteristics of response signals. In consideration of system cross coupling characteristics manifested in coherence and phase coefficients, the skewness and kurtosis tuning steps for each control channel are formulated by using a sequential phase modification method. The relationships between reference skewnesses, kurtoses and spectra are discussed and they reveal that the reference spectra have an influence on the settings of reference skewnesses and kurtoses, which implies that proper settings of reference skewnesses, kurtoses and spectra are necessary. A numerical example and a triaxial vibration test are provided and the results show the validity and feasibility of the proposed method.

Probability distributions control for multi-input multi-output stationary non-Gaussian random vibration test

An inverse system method for multi-input multi-output stationary non-Gaussian random vibration test is proposed in the paper to control the response characteristics both in time-domain and frequency-domain simultaneously. Hence, the control objectives are not only the traditional response power spectral densities but also probability distributions. The control of the probability distributions is more comprehensive and reasonable than the control of kurtoses in order to duplicate the time-domain characteristics of the measured data because kurtoses provide only partial behaviors of the probability distributions. The nonlinear transformation process is introduced to generate non-Gaussian random signals with specified probability distributions. To obtain the desired vibration environments for the test, the reference response signals are synthesized first by the reference spectra and probability distributions, and then the coupled drive signals are generated via the inverse system in the time domain. The close loop correction algorithms are implemented to update the drive signals, actually to update the reference response signals according to the deviations between the references and the measured responses. Finally, a numerical example by a cantilever beam and a biaxial vibration test are carried out and the results demonstrate the effectiveness and feasibility of the proposed method.

Control method for multi-input multi-output non-Gaussian random vibration test with cross spectra consideration

A control method for Multi-Input Multi-Output (MIMO) non-Gaussian random vibration test with cross spectra consideration is proposed in the paper. The aim of the proposed control method is to replicate the specified references composed of auto spectral densities, cross spectral densities and kurtoses on the test article in the laboratory. It is found that the cross spectral densities will bring intractable coupling problems and induce difficulty for the control of the multi-output kurtoses. Hence, a sequential phase modification method is put forward to solve the coupling problems in multi-input multi-output non-Gaussian random vibration test. To achieve the specified responses, an improved zero memory nonlinear transformation is utilized first to modify the Fourier phases of the signals with sequential phase modification method to obtain one frame reference response signals which satisfy the reference spectra and reference kurtoses. Then, an inverse system method is used in frequency domain to obtain the continuous stationary drive signals. At the same time, the matrix power control algorithm is utilized to control the spectra and kurtoses of the response signals further. At the end of the paper, a simulation example with a cantilever beam and a vibration shaker test are implemented and the results support the proposed method very well.

A comparative study on damage analysis between gaussian and non-gaussian random vibration

Vibratory fatigue has been indicated to be one of the most frequently encountered problems in engineering practice. And it is inevitable that the mechanical components of machine are excited by random signals. Most of the random vibrations in nature contain non-Gaussian components. In order to reduce the failure and economic losses which is caused by vibration, random vibration testing is usually conducted in laboratory to verify whether the components can survive a particular random vibration or to identify weaknesses of items. In this paper, the vibratory fatigue damages of Gaussian random signals and non-Gaussian random signals to a particular system are discussed. The process and difference are illustrated by using a case study.

Control Method for Multiple-Input Multiple-Output Non-Gaussian Random Vibration Test

A control method for multi-input multi-output non-Gaussian random vibration test based on an improved zero-memory nonlinear transformation and an inverse system method is proposed. Compared with the classic zero-memory nonlinear transformation method, the improved one can overcome the defect of the dynamic range loss. The inverse system method is put forward in order to control the kurtoses and the spectra for multi-input multi-output non-Gaussian random vibration test simultaneously. The main idea of inverse system method is to generate the Gaussian reference response signals first from the reference spectra, and the improved zero-memory nonlinear transformation method is utilized to obtain the non-Gaussian reference response signals with the reference kurtoses, then the continuous and stationary coupled driving signals can be derived from the relationship between the inputs and outputs of the test system. Thus, the difficulty in generation of driving signals in multi-input multi-output non-Gaussian random vibration test can be overcome. The matrix power control algorithm is introduced for the spectrum control, and a kurtosis control algorithm is set up similarly. A simulation example and an experimental test are provided in the paper, and the results illustrate the effectiveness and feasibility of the proposed control method. Copyright © 2017 John Wiley & Sons, Ltd.