Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

DOI： 10.1016/j.probengmech.2023.103504

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Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Japan Society of Mechanical Engineers  

DOI： 10.1299/transjsme.22-00143

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Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

DOI： 10.1016/j.ijnonlinmec.2022.104208

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Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：ASME International  

Abstract

We present the analytical solutions of the second-, third-, and fourth-order response moments of a single-degree-of-freedom linear system subjected to a class of non-Gaussian random excitation. The non-Gaussian excitation is a zero-mean stationary stochastic process prescribed by an arbitrary probability density and a power spectrum whose peak is located at zero frequency. The excitation is described by an Itô stochastic differential equation in which the drift and diffusion coefficients are determined from the probability density and spectral density of the excitation. In order to obtain the analytical solutions of the response moments, first, we derive the third- and fourth-order autocorrelation functions of the non-Gaussian excitation using its Markov and detailed balance properties. The third-order correlation function is given by the same expression regardless of the difference in the probability density function of the excitation. On the other hand, the fourth-order correlation function is derived under the assumption that the excitation probability density belongs to the Pearson distribution family, which is one of the widest classes of probability distributions. Then, combining the autocorrelation functions of the excitation and the convolution representation of the response, we obtain the exact solutions of the response moments, and it is shown what kind of components the response moments are composed of. Finally, we investigate the dominant time-varying components of the response moments for several different excitation bandwidths.

DOI： 10.1115/1.4055079

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Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

DOI： 10.1007/s00707-022-03264-w

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Other Link： https://link.springer.com/article/10.1007/s00707-022-03264-w/fulltext.html

Authorship：Corresponding author   Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Japan Society of Mechanical Engineers  

DOI： 10.1299/transjsme.21-00047

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Language：English   Publishing type：Research paper (international conference proceedings)  

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Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (international conference proceedings)  

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Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (international conference proceedings)  

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Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (international conference proceedings)  

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Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.11345/nctam.64.103

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Authorship：Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.11345/nctam.64.115

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Authorship：Corresponding author   Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Japan Society of Mechanical Engineers  

DOI： 10.1299/transjsme.17-00586

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Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (international conference proceedings)  

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Authorship：Lead author,　Corresponding author   Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Japan Society of Mechanical Engineers  

<p>Response distribution of a SDOF linear system subjected to non-Gaussian random excitation is investigated. The excitation is modeled by a zero-mean stationary stochastic process prescribed by the non-Gaussian probability density and the power spectrum with bandwidth and dominant frequency parameters. In this paper, we use bimodal and Laplace distributions for the non-Gaussian distribution of the excitation. The excitation is generated numerically by using the Ito stochastic differential equation. Monte Carlo simulations are carried out to obtain the stationary probability densities^ of the system displacement and velocity. It is found that the shape of the response distribution changes depending on a difference in the shape of power spectral density between the excitation and the response. In order to evaluate the difference of the spectral densities quantitatively, a new index is defined. The correspondence of this index to the shape of the response distribution is shown. Next, we compare the present difference index of power spectra and another index which the authors used in the previous study to investigate the response distribution of a non-Gaussian randomly excited system. The comparison shows that when the present index is close to 0, the shape of the response distribution looks like the shape of the excitation distribution. For the index around 0.6, the response distribution becomes the middle shape between the excitation probability density and a Gaussian distribution. In the case of the index greater than 1.2, the response distribution is nearly Gaussian. The difference index of power spectra between the excitation and the response can be calculated readily from the frequency response function of a linear system and the excitation power spectrum, regardless of the excitation probability density function. This index enables us to roughly estimate the shapes of the probability distributions of the displacement and velocity responses without Monte Carlo simulation.</p>

DOI： 10.1299/transjsme.17-00318

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Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (international conference proceedings)  

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Authorship：Lead author,　Corresponding author   Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Japan Society of Mechanical Engineers  

A method based on the minimum cross entropy principle is presented for obtaining approximately the response distributions of nonlinear systems subjected to non-Gaussian random excitation. The response distributions are determined according to the minimization of the cross entropy (or the Kullback-Leibler divergence measure) between an a priori probability density and the estimated probability density under the constraints for the statistical moments of the response. The a priori probability distribution approximates the exact response distribution. In this paper, as the constraint conditions, the moment equations and the normalized condition of the probability density are used, and three types of a priori distributions are given by taking account of the bandwidth ratio between the excitation and the system. In order to demonstrate the validity of the method, a Duffing oscillator subjected to non-Gaussian excitation is analyzed by using the proposed procedure. Bimodal and gamma distributions are used for the excitation distribution. These distributions are highly non-Gaussian, and are different from each other. We compare the analytical results with the results obtained by Monte Carlo simulation and the maximum entropy method. It is shown that the proposed method yields the better approximate solutions than that obtained through the maximum entropy method. The numerical examples indicate the effectiveness of the a priori distribution described in this paper.

DOI： 10.1299/transjsme.15-00528

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Authorship：Corresponding author   Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Japan Society of Mechanical Engineers  

<p>The approximate analytical method using the maximum entropy method (MEM) is proposed to estimate the stationary probability density function of nonlinear systems subjected to non-white random excitation. The MEM is often used to estimate the response distribution of nonlinear systems subjected to Gaussian white noise. In order to obtain the response distribution, the moment equations are used as the constraint conditions on the MEM. However, in the case of nonlinear systems under non-white random excitation, the term of the cross-correlation between the excitation and the response in the moment equations is generally not able to be calculated. In the proposed method, the equivalent linearization technique is applied to calculate the cross-correlation approximately. Using the method, we estimate the stationary response probability density functions of a Duffing oscillator and an asymmetric nonlinear system subjected to non-white excitation with the exponentially decaying correlation function. In the analysis, a wide range of the excitation bandwidth is considered. To demonstrate the effectiveness of the method, the results are compared with those of Monte Carlo simulation.</p>

DOI： 10.1299/transjsme.16-00129

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Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Science Council of Japan  

DOI： 10.11345/nctam.63.81

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Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (international conference proceedings)  

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Authorship：Lead author,　Corresponding author   Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Japan Society of Mechanical Engineers  

This paper presents an application of equivalent non-Gaussian excitation method for the response analysis of systems subjected to non-Gaussian random excitation with an asymmetric probability distribution. The non-Gaussian excitation is prescribed by the probability density function and the power spectrum. The excitation is governed by the Itô stochastic differential equation. Moment equations for the response can be derived from the stochastic differential equation for the excitation and the equation of motion of the system. However, the moment equations are generally not closed due to the nonlinearity of the diffusion coefficient in the stochastic differential equation for the excitation even though the system is linear. In the previous paper, equivalent non-Gaussian excitation method was developed to obtain a closed set of the moment equations. It was demonstrated that for obtaining the variance and kurtosis of the response, the method is applicable to the case of the symmetric non-Gaussian excitation with a wide range of the kurtosis and bandwidth. In this study, equivalent non-Gaussian excitation method is utilized to analyze a linear system subjected to non-Gaussian random excitation with extended generalized Gaussian distribution. The probability distribution can express a variety of asymmetric non-Gaussian distributions with the quite different skewness and kurtosis. The results are compared with those obtained by Monte Carlo simulation. The application in the present paper shows that the method can accurately estimate not only the variance and kurtosis of the response but also the non-zero skewness caused by the asymmetry of the excitation.

DOI： 10.1299/transjsme.15-00163

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Authorship：Corresponding author   Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Japan Society of Mechanical Engineers  

The method using Gaussian mixture model and moment equations is developed to obtain the probability density of the stationary response of a nonlinear system subjected to non-Gaussian random excitation. The excitation is characterized by the probability density function and the power spectrum. In this paper, the stationary response distribution of the system is approximated by the Gaussian mixture model, which is expressed by the weighted sum of several Gaussian distributions with the different parameters. The parameters in the model are determined according to the moment equations for the response and the excitation. The proposed method is applied to a Duffing oscillator subjected to non-Gaussian excitation with the gamma distribution and the power spectral density characterized by the bandwidth parameter. The analytical results of the stationary response distributions are compared with simulation results. The results show this method is valid for the highly skewed excitation with a wide range of the bandwidth parameter. The influences of the shape of the distribution and the bandwidth of the excitation on the response distributions are also investigated.

DOI： 10.1299/transjsme.14-00632

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Authorship：Lead author,　Corresponding author   Language：Japanese   Publishing type：Research paper (international conference proceedings)  

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Authorship：Lead author,　Corresponding author   Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Japan Society of Mechanical Engineers  

Equivalent non-Gaussian excitation method is developed to obtain the statistical moments up to 4th order of the response of non-Gaussian randomly excited systems. The non-Gaussian excitation is prescribed by the probability density function and the power spectrum. The excitation is governed by the Itôstochastic differential equation. Generally, moment equations for the response, which are derived from the stochastic differential equation for the excitation and the equation of motion of the system, are not closed form due to the complex nonlinearity of the diffusion coefficient in the governing equation for the excitation even though the system is linear. In equivalent non-Gaussian excitation method, the diffusion coefficient is replaced with the equivalent diffusion coefficient approximately to obtain a closed set of the moment equations. The square of the equivalent diffusion coefficient is expressed by a second-order polynomial. The coefficients of the polynomial are determined according to the criterion of minimization of the mean square error between the original diffusion coefficient and the equivalent diffusion coefficient. In order to assess the validity of the present method, a linear system subjected to a non-Gaussian random excitation with the generalized Gaussian distribution and the power spectral density with the bandwidth parameter is analyzed. From the comparison with the Monte Carlo simulations, It is shown that for obtaining the variance and the kurtosis of the response, the proposed method is applicable to the case of the non-Gaussian excitation with a wide range of the kurtosis and the bandwidth. In order to discuss the accuracy of the method, the statistical moments of the equivalent non-Gaussian excitation are also investigated.

DOI： 10.1299/transjsme.14-00410

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Institute of Electronics, Information and Communications Engineers (IEICE)  

Nonlinear oscillators driven by correlated noisy signals can synchronize without direct mutual interactions. Here we show that correlation between noisy signals can be enhanced by applying a threshold filter, and the filtered signals can be used to improve noise-induced synchronization. We derive analytical expressions for the correlation coefficient between the filtered signals, and, using simple examples, we demonstrate that the correlation can actually be enhanced and the synchronization can be improved by the threshold filtering in some cases.

DOI： 10.1587/nolta.5.157

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Authorship：Lead author,　Corresponding author   Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Japan Society of Mechanical Engineers  

An envelope distribution approach is developed for generation of narrowband non-Gaussian processes. The processes are prescribed by the probability density and the power spectrum. The proposed approach is based on the method of stochastic differential equation, in which the drift and diffusion coefficients are adjusted to match the given probability distribution and power spectral density. In order to construct the stochastic differential equation, a joint probability distribution which satisfies some conditions is needed. The probability distribution can be obtained from the envelope distribution corresponding to the target non-Gaussian distribution. The proposed approach is applicable to generation of narrowband processes with a variety of non-Gaussian probability densities. Examples are presented to illustrate the usefulness of the approach.

DOI： 10.1299/transjsme.2014dr0100

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Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (international conference proceedings)  

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Authorship：Lead author,　Corresponding author   Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Japan Society of Mechanical Engineers  

Response distribution of an asymmetric nonlinear stiffness system to non-Gaussian random excitation is investigated. The excitation is a stationary stochastic process characterized by the non-Gaussian probability density and the power spectrum with a wide range of bandwidth. Both bimodal and Laplace distributions are considered as the non-Gaussianity of the excitation. A non-Gaussian stochastic process is generated by calculating an Ito stochastic differential equation in which the drift and diffusion coefficients are determined according to the given probability density and spectral density of the process. Monte Carlo simulations are carried out to obtain the stationary response distributions of linear system, Duffing system, and asymmetric stiffness system subjected to the non-Gaussian excitation. It is shown that the response distribution varies markedly depending on the bandwidth and non-Gaussianity of the excitation, and furthermore, the effect of the asymmetry of the system appears clearly in the response distribution.

DOI： 10.1299/kikaic.79.582

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Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (international conference proceedings)  

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Authorship：Lead author,　Corresponding author   Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Japan Society of Mechanical Engineers  

DOI： 10.1299/kikaic.77.4382

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Event date： 2024.9

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