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Vibration response and amplitude frequency characteristics of a controlled nonlinear meso-scale beam under periodic loading are studied. A method including a general analytical expression for harmonic balance solution to periodic vibration and an updated cycle iteration algorithm for amplitude frequency relation of periodic response is developed. A vibration equation with the general expression of nonlinear terms for periodic response is derived and a general analytical expression for harmonic balance solution is obtained. An updated cycle iteration procedure is proposed to obtain amplitude frequency relation. Periodic vibration response with various frequencies can be calculated uniformly using the method. The method can take into account the effect of higher harmonic components on vibration response, and it is applicable to various periodic vibration analyses including principal resonance, super-harmonic resonance, and multiple stationary responses. Numerical results demonstrate that the developed method has good convergence and accuracy. The response amplitude should be determined by the periodic solution with multiple harmonic terms instead of only the first harmonic term. The damping effect on response illustrates that vibration responses of the nonlinear meso beam can be reduced by feedback control with certain damping gain. The amplitude frequency characteristics including anti-resonance and resonant response variation have potential application to the vibration control design of nonlinear meso-scale structure systems.
Zu-Guang Ying; Yi-Qing Ni. Vibrational Amplitude Frequency Characteristics Analysis of a Controlled Nonlinear Meso-Scale Beam. Actuators 2021, 10, 180 .
AMA StyleZu-Guang Ying, Yi-Qing Ni. Vibrational Amplitude Frequency Characteristics Analysis of a Controlled Nonlinear Meso-Scale Beam. Actuators. 2021; 10 (8):180.
Chicago/Turabian StyleZu-Guang Ying; Yi-Qing Ni. 2021. "Vibrational Amplitude Frequency Characteristics Analysis of a Controlled Nonlinear Meso-Scale Beam." Actuators 10, no. 8: 180.
Amplitude frequency characteristics of a controlled nonlinear meso-scale beam are studied. Harmonic balance solution method including general analytical expression and updated cycle iteration procedure is developed. Vibration equation with general expression of nonlinear terms for periodic response is derived and general analytical expression for harmonic balance solution is obtained. Updated cycle iteration procedure for amplitude frequency relation is proposed. Periodic vibration response with various frequencies can be calculated uniformly. The method can take into account effect of higher harmonic components on response, and is applicable to various periodic vibration including principal and super-harmonic resonances. Numerical results demonstrate that the developed method has good convergence and accuracy. Effect of damping gain on vibration response reduction of the beam with feedback control is explored. Anti-resonant response near super-harmonic resonance in the nonlinear beam is obtained. Smaller amplitude response has larger stability probability than larger amplitude response for two stationary responses.
Zuguang Ying; Yiqing Ni; Zhigang Ruan. Damping Effect of a Controlled Nonlinear Meso-Scale Beam Under Periodic Excitation. Advances in Intelligent Automation and Soft Computing 2021, 154 -165.
AMA StyleZuguang Ying, Yiqing Ni, Zhigang Ruan. Damping Effect of a Controlled Nonlinear Meso-Scale Beam Under Periodic Excitation. Advances in Intelligent Automation and Soft Computing. 2021; ():154-165.
Chicago/Turabian StyleZuguang Ying; Yiqing Ni; Zhigang Ruan. 2021. "Damping Effect of a Controlled Nonlinear Meso-Scale Beam Under Periodic Excitation." Advances in Intelligent Automation and Soft Computing , no. : 154-165.
A closed-loop controlled system usually consists of the main structure, sensors, and actuators. The dynamics of sensors and actuators may influence the motion of the main structure. This article presents an analytical study on the first-passage reliability of a nonlinear stochastic controlled system under the consideration of the dynamics of sensors and actuators. The coupled dynamic equations of the controlled systems with sensors and actuators are first given, which are further integrated into a controlled, randomly excited, dissipated Hamiltonian system. By applying the stochastic averaging method for quasi-Hamiltonian systems, a one-dimensional averaged differential equation for the Hamiltonian function is obtained. The backward Kolmogorov equation associated with the averaged equation is then derived for the first-passage reliability analysis, from which the approximate reliability function and probability density of first-passage time are obtained. The accuracy of the proposed procedure is demonstrated by an example. A comparative analysis of the reliability of the system with/without sensors and actuators is carried out, which indicates that ignoring sensors and actuators will make underestimation of the reliability of the closed-loop system with small time. However, when time increases, there appears the opposite trend. Our findings provide a reference for control strategy design.
Sun Jiaojiao; Xia Lei; Ying Zuguang; Huan Ronghua; Zhu Weiqiu. Reliability of nonlinear stochastic controlled systems considering the dynamics of sensors and actuators. Journal of Vibration and Control 2021, 1 .
AMA StyleSun Jiaojiao, Xia Lei, Ying Zuguang, Huan Ronghua, Zhu Weiqiu. Reliability of nonlinear stochastic controlled systems considering the dynamics of sensors and actuators. Journal of Vibration and Control. 2021; ():1.
Chicago/Turabian StyleSun Jiaojiao; Xia Lei; Ying Zuguang; Huan Ronghua; Zhu Weiqiu. 2021. "Reliability of nonlinear stochastic controlled systems considering the dynamics of sensors and actuators." Journal of Vibration and Control , no. : 1.
A multimode perturbation method for frequency response analysis of nonlinearly vibrational beams with periodic distribution parameters is proposed. The partial differential equation with spatial varying parameters for nonlinear vibration of beams with periodic parameters under harmonic excitations is derived. The procedure of the multimode perturbation method includes three main steps: first, the nonlinear partial differential equation is transformed into linear partial differential equations with varying parameters by applying perturbation method; second, the linear partial differential equations are transformed into ordinary differential equations with multimode coupling by applying Galerkin method, where multiple vibration modes of the beams are used and the equations are suitable to nonlinear vibration of periodic structures with high parameter-varying wave in wide frequency band; third, the ordinary differential equations are solved by applying harmonic balance method to obtain vibration response of the nonlinear periodic beam, which is used for characteristics analysis of frequency response and spatial mode. Furthermore, the stability problem of nonlinear harmonic vibration as multidegree-of-freedom system with periodic time-varying parameters is solved by applying direct eigenvalue analysis approach. The proposed method can incorporate multiple vibration modes into response analysis of nonlinear periodic structures and consider mode-coupling effects due to structural nonlinearity and parametric periodicity. Finally, a nonlinear beam with periodic supports under harmonic excitations is studied. Numerical results on frequency response of the beam are given to illustrate an application of the proposed method, new frequency response characteristics, and influences of periodic parameters on structural response. The results have potential application to nonlinear structural vibration control and support damage detection of nonlinear structures with periodic supports.
Zu-Guang Ying; Yi-Qing Ni. A multimode perturbation method for frequency response analysis of nonlinearly vibrational beams with periodic parameters. Journal of Vibration and Control 2019, 26, 1260 -1272.
AMA StyleZu-Guang Ying, Yi-Qing Ni. A multimode perturbation method for frequency response analysis of nonlinearly vibrational beams with periodic parameters. Journal of Vibration and Control. 2019; 26 (13-14):1260-1272.
Chicago/Turabian StyleZu-Guang Ying; Yi-Qing Ni. 2019. "A multimode perturbation method for frequency response analysis of nonlinearly vibrational beams with periodic parameters." Journal of Vibration and Control 26, no. 13-14: 1260-1272.
Some kinds of structures such as continuous girder viaducts and bridges have periodically spaced supports, and their support damage can potentially be detected using the change in extraordinary dynamic characteristics pertinent to quasiperiodic structure dynamics. In this study, the dynamic characteristics of quasiperiodically multisupported beam structures with local weak coupling are explored by using analytical and numerical methods. The eigenvalue equation and analytical expression of characteristic response of the spaced supported beam are first derived using the Galerkin method. For the periodic beam with four supports in particular, the analytical expressions for calculating natural frequencies and vibration modes are obtained. The fundamental frequency loci veering and local weak coupling between spans of the periodic beam are demonstrated, and the critical value of support stiffness is determined. In the case of quasiperiodic beam with four supports, the frequency loci veering and fundamental modal jump are explicitly illustrated through tuning the support stiffness. The modal jump leads to mode localization around the stiffness‐reduced support, which can be used for determining the support damage. Subsequently, a periodically multisupported girder bridge model in consideration of support damage is addressed, where the stiffness reduction due to support damage induces the period detuning. The natural frequency equation and vibration mode expression of the quasiperiodic girder are elicited. Numerical results illustrate some extraordinary dynamic characteristics including the frequency loci veering and nonlinear reliance of the first natural frequency on support stiffness, the fundamental vibration mode alteration and modal jump, the fundamental mode localization, and noticeable change in absolute mode displacement, which can be used to determine the reduction in support stiffness or damage. The analysis method and results on the dynamic characteristics such as mode localization are greatly helpful for determining the support damage of periodically supported structures and identifying the damage location.
Zu‐Guang Ying; Yi‐Qing Ni; Lei Kang. Mode localization characteristics of damaged quasiperiodically supported beam structures with local weak coupling. Structural Control and Health Monitoring 2019, 26, e2351 .
AMA StyleZu‐Guang Ying, Yi‐Qing Ni, Lei Kang. Mode localization characteristics of damaged quasiperiodically supported beam structures with local weak coupling. Structural Control and Health Monitoring. 2019; 26 (6):e2351.
Chicago/Turabian StyleZu‐Guang Ying; Yi‐Qing Ni; Lei Kang. 2019. "Mode localization characteristics of damaged quasiperiodically supported beam structures with local weak coupling." Structural Control and Health Monitoring 26, no. 6: e2351.
An optimal bounded control strategy for smart structure systems as controlled Hamiltonian systems with random excitations and noised observations is proposed. The basic dynamic equations for a smart structure system with smart sensors and actuators are firstly given. The nonlinear stochastic control system with noised observations is then obtained from the simplified smart structure system, and the system is expressed by generalized Hamiltonian equations with control, random excitation and dissipative forces. The optimal control problem for nonlinear stochastic systems with noised observations includes two parts: optimal state estimation and optimal response control based on estimated states, which are coupled each other. The probability density of optimally estimated systems has generally infinite dimensions based on the separation theorem. The proposed optimal control strategy gives an approximate separate solution. First, the optimally estimated system state is determined by the observations based on the extended Kalman filter, and the estimated nonlinear system with controls and stochastic excitations is obtained which has finite-dimensional probability density. Second, the dynamical programming equation for the estimated system is determined based on the stochastic dynamical programming principle. The control boundedness due to actuator saturation is considered, and the optimal bounded control law is obtained by the programming equation with the bounded control constraint. The optimal control depends on the estimated system state which is determined by noised observations. The proposed optimal bounded control strategy is finally applied to a single-degree-of-freedom nonlinear stochastic system with control and noised observation. The remarkable vibration control effectiveness is illustrated with numerical results. Thus the proposed optimal bounded control strategy is promising for application to nonlinear stochastic smart structure systems with noised observations.
Z. G. Ying; W. Q. Zhu. Optimal bounded control for nonlinear stochastic smart structure systems based on extended Kalman filter. Nonlinear Dynamics 2017, 90, 105 -114.
AMA StyleZ. G. Ying, W. Q. Zhu. Optimal bounded control for nonlinear stochastic smart structure systems based on extended Kalman filter. Nonlinear Dynamics. 2017; 90 (1):105-114.
Chicago/Turabian StyleZ. G. Ying; W. Q. Zhu. 2017. "Optimal bounded control for nonlinear stochastic smart structure systems based on extended Kalman filter." Nonlinear Dynamics 90, no. 1: 105-114.
Systems which specifications change abruptly and statistically, referred to as Markovian-jump systems, are considered in this paper. An approximate method is presented to assess the asymptotic stability, with probability one, of nonlinear, multi-degree-of-freedom, Markovian-jump quasi-nonintegrable Hamiltonian systems subjected to stochastic excitations. Using stochastic averaging and linearization, an approximate formula for the largest Lyapunov exponent of the Hamiltonian equations is derived, from which necessary and sufficient conditions for asymptotic stability are obtained for different jump rules. In a Markovian-jump system with unstable operating forms, the stability conditions prescribe limitations on time spent in each unstable form so as to render the entire system asymptotically stable. The validity and utility of this approximate technique are demonstrated by a nonlinear two-degree-of-freedom oscillator that is stochastically driven and capable of Markovian jumps.
R.H. Huan; W.Q. Zhu; F. Ma; Z.G. Ying. Asymptotic stability of a class of nonlinear stochastic systems undergoing Markovian jumps. Probabilistic Engineering Mechanics 2016, 45, 13 -21.
AMA StyleR.H. Huan, W.Q. Zhu, F. Ma, Z.G. Ying. Asymptotic stability of a class of nonlinear stochastic systems undergoing Markovian jumps. Probabilistic Engineering Mechanics. 2016; 45 ():13-21.
Chicago/Turabian StyleR.H. Huan; W.Q. Zhu; F. Ma; Z.G. Ying. 2016. "Asymptotic stability of a class of nonlinear stochastic systems undergoing Markovian jumps." Probabilistic Engineering Mechanics 45, no. : 13-21.
In electric trains, a pantograph is mounted on the roof of the train to collect power through contact with an overhead catenary wire. The carbon-strip suspension of a pantograph, along which contact with the catenary occurs, is subjected to harmonic and stochastic contact-force excitations. In this paper, vertical dynamics of the carbon-strip suspension is studied with an aim of improving the reliability and safety of running trains. A single-degree-of-freedom model of the carbon-strip suspension with nonlinear stiffness is developed using parameter values of the DSA X pantograph. Through stochastic averaging, a Fokker–Planck–Kolmogorov equation governing the stationary response of the carbon-strip suspension is set up. Based on the transition probability density of the stationary response, it is found that random jumps and bifurcations in the carbon-strip motion can occur. The possibility of motion bifurcations and the frequency of random jumps warrant consideration in advanced design of carbon-strip suspensions.
Ronghua Huan; W. Q. Zhu; Fei Ma; Z. G. Ying. Vertical dynamics of a pantograph carbon-strip suspension under stochastic contact-force excitation. Nonlinear Dynamics 2013, 76, 765 -776.
AMA StyleRonghua Huan, W. Q. Zhu, Fei Ma, Z. G. Ying. Vertical dynamics of a pantograph carbon-strip suspension under stochastic contact-force excitation. Nonlinear Dynamics. 2013; 76 (1):765-776.
Chicago/Turabian StyleRonghua Huan; W. Q. Zhu; Fei Ma; Z. G. Ying. 2013. "Vertical dynamics of a pantograph carbon-strip suspension under stochastic contact-force excitation." Nonlinear Dynamics 76, no. 1: 765-776.
A stochastic minimax optimal control strategy for uncertain quasi-Hamiltonian systems is proposed based on the stochastic averaging method, stochastic maximum principle and stochastic differential game theory. First, the partially completed averaged Itô stochastic differential equations are derived from a given system by using the stochastic averaging method for quasi-Hamiltonian systems with uncertain parameters. Then, the stochastic Hamiltonian system for minimax optimal control with a given performance index is established based on the stochastic maximum principle. The worst disturbances are determined by minimizing the Hamiltonian function, and the worst-case optimal controls are obtained by maximizing the minimal Hamiltonian function. The differential equation for adjoint process as a function of system energy is derived from the adjoint equation by using the Itô differential rule. Finally, two examples of controlled uncertain quasi-Hamiltonian systems are worked out to illustrate the application and effectiveness of the proposed control strategy.
R. C. Hu; Z. G. Ying; W. Q. Zhu. Stochastic minimax optimal control strategy for uncertain quasi-Hamiltonian systems using stochastic maximum principle. Structural and Multidisciplinary Optimization 2013, 49, 69 -80.
AMA StyleR. C. Hu, Z. G. Ying, W. Q. Zhu. Stochastic minimax optimal control strategy for uncertain quasi-Hamiltonian systems using stochastic maximum principle. Structural and Multidisciplinary Optimization. 2013; 49 (1):69-80.
Chicago/Turabian StyleR. C. Hu; Z. G. Ying; W. Q. Zhu. 2013. "Stochastic minimax optimal control strategy for uncertain quasi-Hamiltonian systems using stochastic maximum principle." Structural and Multidisciplinary Optimization 49, no. 1: 69-80.
The smart magneto-rheological visco-elastomer (MRVE) has a promising application to vibration control. Its dynamic characteristics are described by complex moduli which are applicable to linear dynamics. However, experimental results show remarkable nonlinear relations between force and deformation for certain large deformations, and the nonlinear dynamic modeling needs to be developed. The present study focuses on the nonlinear dynamic characteristics of MRVE. The MRVE was fabricated and specimens were tested to show nonlinear mechanical properties and dynamic behaviors. The nonlinear effect induced by applied magnetic fields was investigated. A phenomenological model for the dynamic behaviors of MRVE was proposed to describe the nonlinear elasticity, linear damping and hysteretic effect, and the corresponding equivalent linear model in the frequency domain was also given for small deformations. The proposed model is applicable to the dynamics and control analysis of composite structures with MRVE.
Zuguang Ying; Yiqing Ni; Masoud Sajjadi. Nonlinear dynamic characteristics of magneto-rheological visco-elastomers. Science China Technological Sciences 2013, 56, 878 -883.
AMA StyleZuguang Ying, Yiqing Ni, Masoud Sajjadi. Nonlinear dynamic characteristics of magneto-rheological visco-elastomers. Science China Technological Sciences. 2013; 56 (4):878-883.
Chicago/Turabian StyleZuguang Ying; Yiqing Ni; Masoud Sajjadi. 2013. "Nonlinear dynamic characteristics of magneto-rheological visco-elastomers." Science China Technological Sciences 56, no. 4: 878-883.
A stochastic minimax optimal control strategy for partially observable uncertain quasi-Hamiltonian systems is proposed. First, the stochastic optimal control problem of a partially observable nonlinear uncertain quasi-Hamiltonian system is converted into that of a completely observable linear uncertain system based on a theorem due to Charalambous and Elliot. Then, the converted stochastic optimal control problem is solved by a minimax optimal control strategy based on stochastic averaging method and stochastic differential game. The worst-case disturbances and the optimal controls are obtained by solving a Hamilton-Jacobi-Isaacs (HJI) equation. As an example, the stochastic minimax optimal control of a partially observable Duffing–van der Pol oscillator with uncertain disturbances is worked out in detail to illustrate the procedure and effectiveness of the proposed control strategy.
J. Feng; Z.G. Ying; W.Q. Zhu. A minimax optimal control strategy for partially observable uncertain quasi-Hamiltonian systems. International Journal of Non-Linear Mechanics 2012, 47, 1147 -1153.
AMA StyleJ. Feng, Z.G. Ying, W.Q. Zhu. A minimax optimal control strategy for partially observable uncertain quasi-Hamiltonian systems. International Journal of Non-Linear Mechanics. 2012; 47 (10):1147-1153.
Chicago/Turabian StyleJ. Feng; Z.G. Ying; W.Q. Zhu. 2012. "A minimax optimal control strategy for partially observable uncertain quasi-Hamiltonian systems." International Journal of Non-Linear Mechanics 47, no. 10: 1147-1153.
Z.G. Ying; J. Feng; W.Q. Zhu; Y.Q. Ni. Stochastic optimal control analysis of a piezoelectric shell subjected to stochastic boundary perturbations. Smart Structures and Systems 2012, 9, 231 -251.
AMA StyleZ.G. Ying, J. Feng, W.Q. Zhu, Y.Q. Ni. Stochastic optimal control analysis of a piezoelectric shell subjected to stochastic boundary perturbations. Smart Structures and Systems. 2012; 9 (3):231-251.
Chicago/Turabian StyleZ.G. Ying; J. Feng; W.Q. Zhu; Y.Q. Ni. 2012. "Stochastic optimal control analysis of a piezoelectric shell subjected to stochastic boundary perturbations." Smart Structures and Systems 9, no. 3: 231-251.
Z G Ying; Ju Feng; Y Q Ni; W Q Zhu. Electric potential response analysis of a piezoelectric shell under random micro-vibration excitations. Smart Materials and Structures 2011, 20, 1 .
AMA StyleZ G Ying, Ju Feng, Y Q Ni, W Q Zhu. Electric potential response analysis of a piezoelectric shell under random micro-vibration excitations. Smart Materials and Structures. 2011; 20 (10):1.
Chicago/Turabian StyleZ G Ying; Ju Feng; Y Q Ni; W Q Zhu. 2011. "Electric potential response analysis of a piezoelectric shell under random micro-vibration excitations." Smart Materials and Structures 20, no. 10: 1.
Z.G. Ying; W.Q. Zhu; S.Q. Ye; Y.Q. Ni. An accurate substructural synthesis approach to random responses. Structural Engineering and Mechanics 2011, 39, 47 -75.
AMA StyleZ.G. Ying, W.Q. Zhu, S.Q. Ye, Y.Q. Ni. An accurate substructural synthesis approach to random responses. Structural Engineering and Mechanics. 2011; 39 (1):47-75.
Chicago/Turabian StyleZ.G. Ying; W.Q. Zhu; S.Q. Ye; Y.Q. Ni. 2011. "An accurate substructural synthesis approach to random responses." Structural Engineering and Mechanics 39, no. 1: 47-75.
The robustness of non-linear stochastic optimal control for quasi-Hamiltonian systems with uncertain parameters is studied. Based on the independence of uncertain parameters and stochastic excitations, the non-linear stochastic optimal control for the nominal quasi-Hamiltonian system with average-value parameters is first obtained by using the stochastic averaging method and stochastic dynamical programming principle. Then, the means and standard deviations of root-mean-square responses, control effectiveness and control efficiency for the uncertain quasi-Hamiltonian system are calculated by using the stochastic averaging method and the probabilistic analysis. By introducing the sensitivity of the variation coefficients of controlled root-mean-square responses, control effectiveness and control efficiency to those of uncertain parameters, the robustness of the non-linear stochastic optimal control is evaluated. Two examples are given to illustrate the proposed control procedure and its robustness.
Y. Wang; Z.G. Ying; W.Q. Zhu. Robustness of non-linear stochastic optimal control for quasi-Hamiltonian systems with parametric uncertainty. International Journal of Systems Science 2009, 40, 1217 -1227.
AMA StyleY. Wang, Z.G. Ying, W.Q. Zhu. Robustness of non-linear stochastic optimal control for quasi-Hamiltonian systems with parametric uncertainty. International Journal of Systems Science. 2009; 40 (12):1217-1227.
Chicago/Turabian StyleY. Wang; Z.G. Ying; W.Q. Zhu. 2009. "Robustness of non-linear stochastic optimal control for quasi-Hamiltonian systems with parametric uncertainty." International Journal of Systems Science 40, no. 12: 1217-1227.
Y. Wang; Z.G. Ying; W.Q. Zhu. Nonlinear stochastic optimal control of Preisach hysteretic systems. Probabilistic Engineering Mechanics 2009, 24, 255 -264.
AMA StyleY. Wang, Z.G. Ying, W.Q. Zhu. Nonlinear stochastic optimal control of Preisach hysteretic systems. Probabilistic Engineering Mechanics. 2009; 24 (3):255-264.
Chicago/Turabian StyleY. Wang; Z.G. Ying; W.Q. Zhu. 2009. "Nonlinear stochastic optimal control of Preisach hysteretic systems." Probabilistic Engineering Mechanics 24, no. 3: 255-264.
Z.G. Ying; W.Q. Zhu. A stochastic optimal time-delay control for nonlinear structural systems. Structural Engineering and Mechanics 2009, 31, 621 -624.
AMA StyleZ.G. Ying, W.Q. Zhu. A stochastic optimal time-delay control for nonlinear structural systems. Structural Engineering and Mechanics. 2009; 31 (5):621-624.
Chicago/Turabian StyleZ.G. Ying; W.Q. Zhu. 2009. "A stochastic optimal time-delay control for nonlinear structural systems." Structural Engineering and Mechanics 31, no. 5: 621-624.
A new stochastic averaging technique for analyzing the response of a single-degree-of-freedom Preisach hysteretic system with nonlocal memory under stationary Gaussian stochastic excitation is proposed. An equivalent nonhysteretic nonlinear system with amplitude-envelope-dependent damping and stiffness is firstly obtained from the given system by using the generalized harmonic balance technique. The relationship between the amplitude envelope and the energy envelope is then established, and the equivalent damping and stiffness coefficients are expressed as functions of the energy envelope. The available range of the yielding force of the system is extended and also the strong nonlinear stiffness of the system is incorporated so as to improve the response prediction. Finally, an averaged Itô stochastic differential equation for the energy envelope of the system as one-dimensional diffusion process is derived by using the stochastic averaging method of energy envelope, and the Fokker–Planck–Kolmogorov equation associated with the averaged Itô equation is solved to obtain stationary probability densities of the energy envelope and amplitude envelope. The approximate solutions are validated by using the Monte Carlo simulation.
Y. Wang; Z.G. Ying; W.Q. Zhu. Stochastic averaging of energy envelope of Preisach hysteretic systems. Journal of Sound and Vibration 2008, 321, 976 -993.
AMA StyleY. Wang, Z.G. Ying, W.Q. Zhu. Stochastic averaging of energy envelope of Preisach hysteretic systems. Journal of Sound and Vibration. 2008; 321 (3-5):976-993.
Chicago/Turabian StyleY. Wang; Z.G. Ying; W.Q. Zhu. 2008. "Stochastic averaging of energy envelope of Preisach hysteretic systems." Journal of Sound and Vibration 321, no. 3-5: 976-993.
A method for designing optimal bounded control of nonlinear hysteretic systems under externally and parametrically random excitations is presented and illustrated with a numerical example on hysteretic column. The hysteretic system subjected to random excitations is firstly replaced by an equivalent nonlinear non-hysteretic stochastic system. Then, the Itô stochastic differential equation for the total energy of the system as a controlled diffusion process is derived by using the stochastic averaging method of energy envelope. For the semi-infinite time interval ergodic control, the dynamic programming equation is established based on the stochastic dynamical programming principle, and the optimal bounded control law is obtained from this equation under the control constraint. The responses of uncontrolled and controlled hysteretic systems are predicted and used for evaluating control efficacy. The robustness of the optimal bounded control for the hysteretic system with uncertain parameters is further analyzed. Numerical results show that the proposed control method has high efficacy and good robustness.
Y. Wang; Z. G. Ying; W. Q. Zhu. Optimal Bounded Control of Hysteretic Systems under External and Parametrical Random Excitations. Advances in Structural Engineering 2008, 11, 177 -187.
AMA StyleY. Wang, Z. G. Ying, W. Q. Zhu. Optimal Bounded Control of Hysteretic Systems under External and Parametrical Random Excitations. Advances in Structural Engineering. 2008; 11 (2):177-187.
Chicago/Turabian StyleY. Wang; Z. G. Ying; W. Q. Zhu. 2008. "Optimal Bounded Control of Hysteretic Systems under External and Parametrical Random Excitations." Advances in Structural Engineering 11, no. 2: 177-187.
A stochastic optimal control strategy for partially observable nonlinear quasi-Hamiltonian systems is proposed. The optimal control force consists of two parts. The first part is determined by the conditions under which the stochastic optimal control problem of a partially observable nonlinear system is converted into that of a completely observable linear system. The second part is determined by solving the dynamical programming equation derived by applying the stochastic averaging method and stochastic dynamical programming principle to the completely observable linear control system. The response of the optimally controlled quasi-Hamiltonian system is predicted by solving the averaged Fokker–Planck–Kolmogorov equation associated with the optimally controlled completely observable linear system and solving the Riccati equation for the estimate errors of system states. An example is given to illustrate the procedure and effectiveness of the proposed control strategy.
Z.G. Ying; W.Q. Zhu. A stochastic optimal control strategy for partially observable nonlinear quasi-Hamiltonian systems. Journal of Sound and Vibration 2008, 310, 184 -196.
AMA StyleZ.G. Ying, W.Q. Zhu. A stochastic optimal control strategy for partially observable nonlinear quasi-Hamiltonian systems. Journal of Sound and Vibration. 2008; 310 (1-2):184-196.
Chicago/Turabian StyleZ.G. Ying; W.Q. Zhu. 2008. "A stochastic optimal control strategy for partially observable nonlinear quasi-Hamiltonian systems." Journal of Sound and Vibration 310, no. 1-2: 184-196.