The Experts below are selected from a list of 318 Experts worldwide ranked by ideXlab platform
Zhilong Huang - One of the best experts on this subject based on the ideXlab platform.
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explicit expression of stationary Response Probability density for nonlinear stochastic systems
Acta Mechanica, 2021Co-Authors: Xiaoling Jin, Yanping Tian, Yong Wang, Zhilong HuangAbstract:Identifying the exactly or approximately explicit expression of the stationary Response Probability density for general nonlinear stochastic dynamical systems is of great significance in the fields of stochastic dynamics and control. Almost all the existing methods are devoted to determine the exact or approximate solution for specific values of system and excitation parameters. Herein, aimed at stochastic systems with polynomial nonlinearity and excited by Gaussian white noises, a novel method is proposed to identify the stationary Response Probability density which explicitly includes system and excitation parameters. The stationary Probability density is first written as an exponential function according to the maximum entropy principle, the power of the exponential function is then expressed as a linear combination of prescribed nondimensional parameter clusters constituted by system and excitation parameters, and state variables, with the coefficients to be determined. The undetermined coefficients are derived by minimizing the residual of the associated Fokker-Planck- Kolmogorov equation. The application and efficacy of the proposed method are illustrated by a typical numerical example.
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identifying explicit expression of Response Probability density of nonlinear stochastic system information theoretic method
Mechanical Systems and Signal Processing, 2020Co-Authors: Yanping Tian, Xiaoling Jin, Yong Wang, Zhilong HuangAbstract:Abstract For a general nonlinear stochastic system, the Response Probability density possesses crucial significance for Response evaluation and reliability design. The existing literatures derive the Response Probability density by accurately or approximately solving the Fokker-Planck- Kolmogorov equation, by searching for the equivalent system according to some criterion and approximating the Probability density of the original system by that of the equivalent one, or by numerically solving the original equation of motion and giving discrete information statistically. Herein, a novel procedure is established to identify the explicit expression of the stationary Response Probability density of a general nonlinear system directly from the discrete data of samples. The stationary Probability density is expressed as an exponent form with the exponential power being linear combination of base functions elaborately selected. The Shannon information entropy is then arranged as a nonlinear function of the statistical moments of base functions which are evaluated by the discrete data of samples. The undetermined coefficients of base functions are finally determined by minimizing the Shannon information entropy. Three typical examples, i.e., Duffing oscillator, van der Pol system and a frictional system (as representatives of smooth systems, electric systems and non-smooth systems, respectively), are investigated to illustrate the accuracy of this procedure, the robustness to data noise, the insensitivity to sampling interval and strength of nonlinearity, and the low requirement on the amount of data.
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Stationary Response Probability density of nonlinear random vibrating systems: a data-driven method
Nonlinear Dynamics, 2020Co-Authors: Yanping Tian, Yong Wang, Zhilong Huang, Hanqing Jiang, Isaac Elishakoff, Guoqiang CaiAbstract:A data-driven method is established to derive the (approximately) analytical expression of the stationary Response Probability density of nonlinear random vibrating system, which explicitly includes system features and intensity of excitation. The stationary Response Probability density is first assumed as an exponential form by using the principle of maximum entropy. Through the rule of dimensional consistency, the power of exponential function is expressed as a linear combination of a set of nondimensional parameter clusters which are constituted by system features, intensity of excitation, and state variables. By comparing the power of exponential function with the approximate logarithm Probability density evaluated from simulated data statistically, the determination of unknown coefficients comes down to the solution of (overdetermined) simultaneous linear algebraic equations. The data-driven method rediscovers the exact stationary Response Probability density of random-excited Duffing oscillator and derives an approximately analytical expression of stationary Response Probability density of van der Pol system from the simulated data of six cases with different values of system features and intensity of excitation. This data-driven method is a unique method which can explicitly include the information of system and excitation in the analytical expression of stationary Response Probability density. It avoids the solution of simultaneous nonlinear algebraic equations encountered in the maximum entropy method and closure methods and, in the meanwhile, avoids the sophisticated selection of weighting functions in closure methods.
Yanping Tian - One of the best experts on this subject based on the ideXlab platform.
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explicit expression of stationary Response Probability density for nonlinear stochastic systems
Acta Mechanica, 2021Co-Authors: Xiaoling Jin, Yanping Tian, Yong Wang, Zhilong HuangAbstract:Identifying the exactly or approximately explicit expression of the stationary Response Probability density for general nonlinear stochastic dynamical systems is of great significance in the fields of stochastic dynamics and control. Almost all the existing methods are devoted to determine the exact or approximate solution for specific values of system and excitation parameters. Herein, aimed at stochastic systems with polynomial nonlinearity and excited by Gaussian white noises, a novel method is proposed to identify the stationary Response Probability density which explicitly includes system and excitation parameters. The stationary Probability density is first written as an exponential function according to the maximum entropy principle, the power of the exponential function is then expressed as a linear combination of prescribed nondimensional parameter clusters constituted by system and excitation parameters, and state variables, with the coefficients to be determined. The undetermined coefficients are derived by minimizing the residual of the associated Fokker-Planck- Kolmogorov equation. The application and efficacy of the proposed method are illustrated by a typical numerical example.
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identifying explicit expression of Response Probability density of nonlinear stochastic system information theoretic method
Mechanical Systems and Signal Processing, 2020Co-Authors: Yanping Tian, Xiaoling Jin, Yong Wang, Zhilong HuangAbstract:Abstract For a general nonlinear stochastic system, the Response Probability density possesses crucial significance for Response evaluation and reliability design. The existing literatures derive the Response Probability density by accurately or approximately solving the Fokker-Planck- Kolmogorov equation, by searching for the equivalent system according to some criterion and approximating the Probability density of the original system by that of the equivalent one, or by numerically solving the original equation of motion and giving discrete information statistically. Herein, a novel procedure is established to identify the explicit expression of the stationary Response Probability density of a general nonlinear system directly from the discrete data of samples. The stationary Probability density is expressed as an exponent form with the exponential power being linear combination of base functions elaborately selected. The Shannon information entropy is then arranged as a nonlinear function of the statistical moments of base functions which are evaluated by the discrete data of samples. The undetermined coefficients of base functions are finally determined by minimizing the Shannon information entropy. Three typical examples, i.e., Duffing oscillator, van der Pol system and a frictional system (as representatives of smooth systems, electric systems and non-smooth systems, respectively), are investigated to illustrate the accuracy of this procedure, the robustness to data noise, the insensitivity to sampling interval and strength of nonlinearity, and the low requirement on the amount of data.
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Stationary Response Probability density of nonlinear random vibrating systems: a data-driven method
Nonlinear Dynamics, 2020Co-Authors: Yanping Tian, Yong Wang, Zhilong Huang, Hanqing Jiang, Isaac Elishakoff, Guoqiang CaiAbstract:A data-driven method is established to derive the (approximately) analytical expression of the stationary Response Probability density of nonlinear random vibrating system, which explicitly includes system features and intensity of excitation. The stationary Response Probability density is first assumed as an exponential form by using the principle of maximum entropy. Through the rule of dimensional consistency, the power of exponential function is expressed as a linear combination of a set of nondimensional parameter clusters which are constituted by system features, intensity of excitation, and state variables. By comparing the power of exponential function with the approximate logarithm Probability density evaluated from simulated data statistically, the determination of unknown coefficients comes down to the solution of (overdetermined) simultaneous linear algebraic equations. The data-driven method rediscovers the exact stationary Response Probability density of random-excited Duffing oscillator and derives an approximately analytical expression of stationary Response Probability density of van der Pol system from the simulated data of six cases with different values of system features and intensity of excitation. This data-driven method is a unique method which can explicitly include the information of system and excitation in the analytical expression of stationary Response Probability density. It avoids the solution of simultaneous nonlinear algebraic equations encountered in the maximum entropy method and closure methods and, in the meanwhile, avoids the sophisticated selection of weighting functions in closure methods.
Michael D Larsen - One of the best experts on this subject based on the ideXlab platform.
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a simple method of sample size calculation for linear and logistic regression
Statistics in Medicine, 1998Co-Authors: F Y Hsieh, Daniel A Bloch, Michael D LarsenAbstract:A sample size calculation for logistic regression involves complicated formulae. This paper suggests use of sample size formulae for comparing means or for comparing proportions in order to calculate the required sample size for a simple logistic regression model. One can then adjust the required sample size for a multiple logistic regression model by a variance inflation factor. This method requires no assumption of low Response Probability in the logistic model as in a previous publication. One can similarly calculate the sample size for linear regression models. This paper also compares the accuracy of some existing sample-size software for logistic regression with computer power simulations. An example illustrates the methods.
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a simple method of sample size calculation for linear and logistic regression
Statistics in Medicine, 1998Co-Authors: F Y Hsieh, Daniel A Bloch, Michael D LarsenAbstract:SUMMARY A sample size calculation for logistic regression involves complicated formulae. This paper suggests use of sample size formulae for comparing means or for comparing proportions in order to calculate the required sample size for a simple logistic regression model. One can then adjust the required sample size for a multiple logistic regression model by a variance inflation factor. This method requires no assumption of low Response Probability in the logistic model as in a previous publication. One can similarly calculate the sample size for linear regression models. This paper also compares the accuracy of some existing sample-size software for logistic regression with computer power simulations. An example illustrates the methods. ( 1998 John Wiley & Sons, Ltd.
Hiroto Ogawa - One of the best experts on this subject based on the ideXlab platform.
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Crickets alter wind-elicited escape strategies depending on acoustic context
Scientific Reports, 2017Co-Authors: Matasaburo Fukutomi, Hiroto OgawaAbstract:Acoustic signals trigger various behaviours in insects such as courtship or escape from predators. However, it remains unknown whether insects utilize acoustic signals to recognize environmental contexts. The cricket is a prominent model insect for neuroethological studies on acoustic behaviour because female crickets exhibit positive phonotaxis in Response to male calling songs, and flying crickets display avoidance behaviour for high-frequency sounds such as echolocation call of bats. The carrier frequency of these sounds is a major factor in determining whether they initiate these acoustic behaviours. Here, we examined the impacts of different frequencies of tone sounds on cercal-mediated escape behaviour, using a 5-kHz tone corresponding to the calling song and a 15-kHz tone serving as a trigger of avoidance behaviours. Neither frequency elicited a Response in the standing cricket by itself, but they had different impacts on walking Responses to airflow stimuli. While the 15-kHz tone reduced Response Probability, extended moving distance, and enhanced turn-angle variability, the 5-kHz tone had no effect. Although both frequencies of tones facilitated walking backward, the 15-kHz tone had a larger effect than the 5-kHz tone. These frequency dependencies of behavioural modulation suggest that crickets can recognize acoustic contexts and alter their escape strategy accordingly.
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auditory modulation of wind elicited walking behavior in the cricket gryllus bimaculatus
The Journal of Experimental Biology, 2015Co-Authors: Matasaburo Fukutomi, Makoto Someya, Hiroto OgawaAbstract:Animals flexibly change their locomotion triggered by an identical stimulus depending on the environmental context and behavioral state. This indicates that additional sensory inputs in different modality from the stimulus triggering the escape Response affect the neuronal circuit governing that behavior. However, how the spatio-temporal relationships between these two stimuli effect a behavioral change remains unknown. We studied this question, using crickets, which respond to a short air-puff by oriented walking activity mediated by the cercal sensory system. In addition, an acoustic stimulus, such as conspecific 'song' received by the tympanal organ, elicits a distinct oriented locomotion termed phonotaxis. In this study, we examined the cross-modal effects on wind-elicited walking when an acoustic stimulus was preceded by an air-puff and tested whether the auditory modulation depends on the coincidence of the direction of both stimuli. A preceding 10 kHz pure tone biased the wind-elicited walking in a backward direction and elevated a threshold of the wind-elicited Response, whereas other movement parameters, including turn angle, reaction time, walking speed and distance were unaffected. The auditory modulations, however, did not depend on the coincidence of the stimulus directions. A preceding sound consistently altered the wind-elicited walking direction and Response Probability throughout the experimental sessions, meaning that the auditory modulation did not result from previous experience or associative learning. These results suggest that the cricket nervous system is able to integrate auditory and air-puff stimuli, and modulate the wind-elicited escape behavior depending on the acoustic context.
Yong Wang - One of the best experts on this subject based on the ideXlab platform.
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explicit expression of stationary Response Probability density for nonlinear stochastic systems
Acta Mechanica, 2021Co-Authors: Xiaoling Jin, Yanping Tian, Yong Wang, Zhilong HuangAbstract:Identifying the exactly or approximately explicit expression of the stationary Response Probability density for general nonlinear stochastic dynamical systems is of great significance in the fields of stochastic dynamics and control. Almost all the existing methods are devoted to determine the exact or approximate solution for specific values of system and excitation parameters. Herein, aimed at stochastic systems with polynomial nonlinearity and excited by Gaussian white noises, a novel method is proposed to identify the stationary Response Probability density which explicitly includes system and excitation parameters. The stationary Probability density is first written as an exponential function according to the maximum entropy principle, the power of the exponential function is then expressed as a linear combination of prescribed nondimensional parameter clusters constituted by system and excitation parameters, and state variables, with the coefficients to be determined. The undetermined coefficients are derived by minimizing the residual of the associated Fokker-Planck- Kolmogorov equation. The application and efficacy of the proposed method are illustrated by a typical numerical example.
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identifying explicit expression of Response Probability density of nonlinear stochastic system information theoretic method
Mechanical Systems and Signal Processing, 2020Co-Authors: Yanping Tian, Xiaoling Jin, Yong Wang, Zhilong HuangAbstract:Abstract For a general nonlinear stochastic system, the Response Probability density possesses crucial significance for Response evaluation and reliability design. The existing literatures derive the Response Probability density by accurately or approximately solving the Fokker-Planck- Kolmogorov equation, by searching for the equivalent system according to some criterion and approximating the Probability density of the original system by that of the equivalent one, or by numerically solving the original equation of motion and giving discrete information statistically. Herein, a novel procedure is established to identify the explicit expression of the stationary Response Probability density of a general nonlinear system directly from the discrete data of samples. The stationary Probability density is expressed as an exponent form with the exponential power being linear combination of base functions elaborately selected. The Shannon information entropy is then arranged as a nonlinear function of the statistical moments of base functions which are evaluated by the discrete data of samples. The undetermined coefficients of base functions are finally determined by minimizing the Shannon information entropy. Three typical examples, i.e., Duffing oscillator, van der Pol system and a frictional system (as representatives of smooth systems, electric systems and non-smooth systems, respectively), are investigated to illustrate the accuracy of this procedure, the robustness to data noise, the insensitivity to sampling interval and strength of nonlinearity, and the low requirement on the amount of data.
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Stationary Response Probability density of nonlinear random vibrating systems: a data-driven method
Nonlinear Dynamics, 2020Co-Authors: Yanping Tian, Yong Wang, Zhilong Huang, Hanqing Jiang, Isaac Elishakoff, Guoqiang CaiAbstract:A data-driven method is established to derive the (approximately) analytical expression of the stationary Response Probability density of nonlinear random vibrating system, which explicitly includes system features and intensity of excitation. The stationary Response Probability density is first assumed as an exponential form by using the principle of maximum entropy. Through the rule of dimensional consistency, the power of exponential function is expressed as a linear combination of a set of nondimensional parameter clusters which are constituted by system features, intensity of excitation, and state variables. By comparing the power of exponential function with the approximate logarithm Probability density evaluated from simulated data statistically, the determination of unknown coefficients comes down to the solution of (overdetermined) simultaneous linear algebraic equations. The data-driven method rediscovers the exact stationary Response Probability density of random-excited Duffing oscillator and derives an approximately analytical expression of stationary Response Probability density of van der Pol system from the simulated data of six cases with different values of system features and intensity of excitation. This data-driven method is a unique method which can explicitly include the information of system and excitation in the analytical expression of stationary Response Probability density. It avoids the solution of simultaneous nonlinear algebraic equations encountered in the maximum entropy method and closure methods and, in the meanwhile, avoids the sophisticated selection of weighting functions in closure methods.
