For the purpose of improving the mechanical performance indices of uncertain structures with interval parameters and ensure their robustness when fluctuating under interval parameters, a constrained interval robust op...For the purpose of improving the mechanical performance indices of uncertain structures with interval parameters and ensure their robustness when fluctuating under interval parameters, a constrained interval robust optimization model is constructed with both the center and halfwidth of the most important mechanical performance index described as objective functions and the other requirements on the mechanical performance indices described as constraint functions. To locate the optimal solution of objective and feasibility robustness, a new concept of interval violation vector and its calculation formulae corresponding to different constraint functions are proposed. The math?ematical formulae for calculating the feasibility and objective robustness indices and the robustness?based preferential guidelines are proposed for directly ranking various design vectors, which is realized by an algorithm integrating Kriging and nested genetic algorithm. The validity of the proposed method and its superiority to present interval optimization approaches are demonstrated by a numerical example. The robust optimization of the upper beam in a high?speed press with interval material properties demonstrated the applicability and effectiveness of the proposed method in engineering.展开更多
The global stabilization problem of nonlinear systems with uncertain structure is dealt with. Based on control Lyapunov function （CLF）, a sufficient and necessary condition for Lyapunov stabilization is given. From ...The global stabilization problem of nonlinear systems with uncertain structure is dealt with. Based on control Lyapunov function （CLF）, a sufficient and necessary condition for Lyapunov stabilization is given. From the condition, several simply sufficient conditions for the globally asymptotical stability are deduced. A state feedback control law is designed to globally asymptotically stabilize the equilibrium of the closed system. Last, a simulation shows the effectiveness of the method.展开更多
Prediction of vibration energy responses of structures with uncertainties is of interest in many fields. The energy density control equation for one-dimensional structure is provided firstly. Interval analysis method ...Prediction of vibration energy responses of structures with uncertainties is of interest in many fields. The energy density control equation for one-dimensional structure is provided firstly. Interval analysis method is applied to the control equation to obtain the range of energy density responses of structures with interval parameters. A cantilever beam with interval-valued damping coefficient is exemplified to carry out a simulation. The result shows that the mean value of energy density from the interval analysis method is the same as that from a probabilistic method which validates the interval analysis method. Besides, the response range from the interval analysis method is wider and includes that from the probabilistic method which indicates the interval analysis method is a more conservative method and is safer in realistic engineering structures.展开更多
An integral analytic process from quantification to propagation based on limited uncertain parameters is investigated to deal with practical engineering problems. A new method by use of the smallest interval-set/hyper...An integral analytic process from quantification to propagation based on limited uncertain parameters is investigated to deal with practical engineering problems. A new method by use of the smallest interval-set/hyper-rectangle containing all exper- imental data is proposed to quantify the parameter uncertainties. With the smallest parameter interval-set, the uncertainty sponse and the least favorable response propagation evaluation of the most favorable re- of the structures is studied based on the interval analysis. The relationship between the proposed interval analysis method （IAM） and the classical IAM is discussed. Two numerical examples are presented to demonstrate the feasibility and validity of the proposed method.展开更多
To study the approximation theory of real sliding mode and the design of variable structure controller for time-invariant linear uncertain time-delay singular system,the approximation theory of real sliding mode was d...To study the approximation theory of real sliding mode and the design of variable structure controller for time-invariant linear uncertain time-delay singular system,the approximation theory of real sliding mode was developed to provide foundation for obtaining sliding mode by equivalent control,and switching functions with integral dynamic compensators and variable structure controllers were designed respectively under two circumstances that the system without uncertain part was stabilized by delay-dependent and delay-independent linear state feedback. The design guarantees the asymptotical stablity of switching manifolds,and the variable structure controllers can force solution trajectory of the system to arrive at the switching manifolds in limited time. A numerical example is given to demonstrate the feasibility and simplicity of the design method.展开更多
In this paper, based on the second-order Taylor series expansion and the difference of convex functions algo- rithm for quadratic problems with box constraints （the DCA for QB）, a new method is proposed to solve the...In this paper, based on the second-order Taylor series expansion and the difference of convex functions algo- rithm for quadratic problems with box constraints （the DCA for QB）, a new method is proposed to solve the static response problem of structures with fairly large uncertainties in interval parameters. Although current methods are effective for solving the static response problem of structures with interval parameters with small uncertainties, these methods may fail to estimate the region of the static response of uncertain structures if the uncertainties in the parameters are fairly large. To resolve this problem, first, the general expression of the static response of structures in terms of structural parameters is derived based on the second-order Taylor series expansion. Then the problem of determining the bounds of the static response of uncertain structures is transformed into a series of quadratic problems with box constraints. These quadratic problems with box constraints can be solved using the DCA approach effectively. The numerical examples are given to illustrate the accuracy and the efficiency of the proposed method when comparing with other existing methods.展开更多
An optimal control procedure is developed for the front and rear wheels of a three-axle vehicle moving on a complex typical road based on model following variable structure control strategy. The actual vehicle may be ...An optimal control procedure is developed for the front and rear wheels of a three-axle vehicle moving on a complex typical road based on model following variable structure control strategy. The actual vehicle may be considered as an uncertain system. Cornering stiffness of front and rear wheels and external disturbances are varied in a limited range. The model-following variable structure control method is used to control both front and rear wheels steering operations of the vehicle, so that steering responses of the vehicle follow from those of the reference model. By numerical results obtained from computer simulation, it is demonstrated that the control system model can cope with the effects of parameter perturbations and outside disturbances.展开更多
PID(proportional-integral-derivative)control is recognized to be the most widely and successfully employed control strategy by far.However,there are limited theoretical investigations explaining the rationale why PID ...PID(proportional-integral-derivative)control is recognized to be the most widely and successfully employed control strategy by far.However,there are limited theoretical investigations explaining the rationale why PID can work so well when dealing with nonlinear uncertain systems.This paper continues the previous researches towards establishing a theoretical foundation of PID control,by studying the regulation problem of PID control for nonaffine uncertain nonlinear stochastic systems.To be specific,a three dimensional parameter set will be constructed explicitly based on some prior knowledge on bounds of partial derivatives of both the drift and diffusion terms.It will be shown that the closed-loop control system will achieve exponential stability in the mean square sense under PID control,whenever the controller parameters are chosen from the constructed parameter set.Moreover,similar results can also be obtained for PD(PI)control in some special cases.A numerical example will be provided to illustrate the theoretical results.展开更多
Traditional reliability analysis requires probability distributions of all the uncertain parameters.However,in many practical applications,the variation bounds can be only determined for the parameters with limited in...Traditional reliability analysis requires probability distributions of all the uncertain parameters.However,in many practical applications,the variation bounds can be only determined for the parameters with limited information.A complex hybrid reliability problem then will be caused when the random and interval variables coexist in a same structure.In this paper,by introducing the response surface technique,we develop a new hybrid reliability method to efficiently compute the interval of the failure probability of the structure due to the probability-interval hybrid uncertainty.The present method consists of a sequence of iterations.At each step,a response surface model is constructed for the limit-state function by using a quadratic polynomial and a modified axial experimental design method.An approximate hybrid reliability problem is created based on the response surface model,which is subsequently solved by an efficient decoupling approach.An updating strategy is suggested to improve the quality of the response surface and whereby ensure the reliability analysis precision.A computational procedure is then summarized for the whole iterations.Four numerical examples and also a practical application are provided to demonstrate the effectiveness of the present method.展开更多
The classical probabilistic reliability theory and fuzzy reliability theory cannot directly measure the uncertainty of structural reliability with uncertain variables, i.e., subjective random and fuzzy variables. In o...The classical probabilistic reliability theory and fuzzy reliability theory cannot directly measure the uncertainty of structural reliability with uncertain variables, i.e., subjective random and fuzzy variables. In order to simultaneously satisfy the duality of randomness and subadditivity of fuzziness in the reliability problem, a new quantification method for the reliability of structures is presented based on uncertainty theory, and an uncertainty-theory-based perspective of classical Cornell reliability index is explored. In this paper, by introducing the uncertainty theory, we adopt the uncertain measure to quantify the reliability of structures for the subjective probability or fuzzy variables, instead of probabilistic and possibilistic measures. We utilize uncertain variables to uniformly represent the subjective random and fuzzy parameters, based on which we derive solutions to analyze the uncertainty reliability of structures with uncertainty distributions. Moreover, we propose the Cornell uncertainty reliability index based on the uncertain expected value and variance.Experimental results on three numerical applications demonstrate the validity of the proposed method.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.51775491,51475417,U1608256,51405433)
文摘For the purpose of improving the mechanical performance indices of uncertain structures with interval parameters and ensure their robustness when fluctuating under interval parameters, a constrained interval robust optimization model is constructed with both the center and halfwidth of the most important mechanical performance index described as objective functions and the other requirements on the mechanical performance indices described as constraint functions. To locate the optimal solution of objective and feasibility robustness, a new concept of interval violation vector and its calculation formulae corresponding to different constraint functions are proposed. The math?ematical formulae for calculating the feasibility and objective robustness indices and the robustness?based preferential guidelines are proposed for directly ranking various design vectors, which is realized by an algorithm integrating Kriging and nested genetic algorithm. The validity of the proposed method and its superiority to present interval optimization approaches are demonstrated by a numerical example. The robust optimization of the upper beam in a high?speed press with interval material properties demonstrated the applicability and effectiveness of the proposed method in engineering.
基金This project was supported by the National Natural Science Foundation of Fujian province (A0510025) .
文摘The global stabilization problem of nonlinear systems with uncertain structure is dealt with. Based on control Lyapunov function （CLF）, a sufficient and necessary condition for Lyapunov stabilization is given. From the condition, several simply sufficient conditions for the globally asymptotical stability are deduced. A state feedback control law is designed to globally asymptotically stabilize the equilibrium of the closed system. Last, a simulation shows the effectiveness of the method.
基金Sponsored by the National Natural Science Foundation of China(Grant No.11072066)
文摘Prediction of vibration energy responses of structures with uncertainties is of interest in many fields. The energy density control equation for one-dimensional structure is provided firstly. Interval analysis method is applied to the control equation to obtain the range of energy density responses of structures with interval parameters. A cantilever beam with interval-valued damping coefficient is exemplified to carry out a simulation. The result shows that the mean value of energy density from the interval analysis method is the same as that from a probabilistic method which validates the interval analysis method. Besides, the response range from the interval analysis method is wider and includes that from the probabilistic method which indicates the interval analysis method is a more conservative method and is safer in realistic engineering structures.
基金Project supported by the National Natural Science Foundation of China (No. 11002013)the 111 Project (No. B07009)the Defense Industrial Technology Development Program of China(Nos. A2120110001 and B2120110011)
文摘An integral analytic process from quantification to propagation based on limited uncertain parameters is investigated to deal with practical engineering problems. A new method by use of the smallest interval-set/hyper-rectangle containing all exper- imental data is proposed to quantify the parameter uncertainties. With the smallest parameter interval-set, the uncertainty sponse and the least favorable response propagation evaluation of the most favorable re- of the structures is studied based on the interval analysis. The relationship between the proposed interval analysis method （IAM） and the classical IAM is discussed. Two numerical examples are presented to demonstrate the feasibility and validity of the proposed method.
基金Sponsored by the National Natural Science Foundation of China (Grant No.60574005)Natural Science Foundation of Qingdao(Grant No.04-2-Jz-98)
文摘To study the approximation theory of real sliding mode and the design of variable structure controller for time-invariant linear uncertain time-delay singular system,the approximation theory of real sliding mode was developed to provide foundation for obtaining sliding mode by equivalent control,and switching functions with integral dynamic compensators and variable structure controllers were designed respectively under two circumstances that the system without uncertain part was stabilized by delay-dependent and delay-independent linear state feedback. The design guarantees the asymptotical stablity of switching manifolds,and the variable structure controllers can force solution trajectory of the system to arrive at the switching manifolds in limited time. A numerical example is given to demonstrate the feasibility and simplicity of the design method.
基金supported by the National Natural Science Foundation of China (Grants 11002013, 11372025)the Defense Industrial Technology Development Program (Grants A0820132001, JCKY2013601B)+1 种基金the Aeronautical Science Foundation of China (Grant 2012ZA51010)111 Project (Grant B07009) for support
文摘In this paper, based on the second-order Taylor series expansion and the difference of convex functions algo- rithm for quadratic problems with box constraints （the DCA for QB）, a new method is proposed to solve the static response problem of structures with fairly large uncertainties in interval parameters. Although current methods are effective for solving the static response problem of structures with interval parameters with small uncertainties, these methods may fail to estimate the region of the static response of uncertain structures if the uncertainties in the parameters are fairly large. To resolve this problem, first, the general expression of the static response of structures in terms of structural parameters is derived based on the second-order Taylor series expansion. Then the problem of determining the bounds of the static response of uncertain structures is transformed into a series of quadratic problems with box constraints. These quadratic problems with box constraints can be solved using the DCA approach effectively. The numerical examples are given to illustrate the accuracy and the efficiency of the proposed method when comparing with other existing methods.
文摘An optimal control procedure is developed for the front and rear wheels of a three-axle vehicle moving on a complex typical road based on model following variable structure control strategy. The actual vehicle may be considered as an uncertain system. Cornering stiffness of front and rear wheels and external disturbances are varied in a limited range. The model-following variable structure control method is used to control both front and rear wheels steering operations of the vehicle, so that steering responses of the vehicle follow from those of the reference model. By numerical results obtained from computer simulation, it is demonstrated that the control system model can cope with the effects of parameter perturbations and outside disturbances.
基金supported by the National Natural Science Foundation of China under Grant No.12288201.
文摘PID(proportional-integral-derivative)control is recognized to be the most widely and successfully employed control strategy by far.However,there are limited theoretical investigations explaining the rationale why PID can work so well when dealing with nonlinear uncertain systems.This paper continues the previous researches towards establishing a theoretical foundation of PID control,by studying the regulation problem of PID control for nonaffine uncertain nonlinear stochastic systems.To be specific,a three dimensional parameter set will be constructed explicitly based on some prior knowledge on bounds of partial derivatives of both the drift and diffusion terms.It will be shown that the closed-loop control system will achieve exponential stability in the mean square sense under PID control,whenever the controller parameters are chosen from the constructed parameter set.Moreover,similar results can also be obtained for PD(PI)control in some special cases.A numerical example will be provided to illustrate the theoretical results.
基金supported by the National Science Foundation for Excellent Young Scholars(Grant No.51222502)the Key Project of Chinese National Programs for Fundamental Research and Development(Grant No.2010CB832700)+1 种基金the National Natural Science Foundation of China(Grant No.11172096)the Key Program of the National Natural Science Foundation of China(Grant No.11232004)
文摘Traditional reliability analysis requires probability distributions of all the uncertain parameters.However,in many practical applications,the variation bounds can be only determined for the parameters with limited information.A complex hybrid reliability problem then will be caused when the random and interval variables coexist in a same structure.In this paper,by introducing the response surface technique,we develop a new hybrid reliability method to efficiently compute the interval of the failure probability of the structure due to the probability-interval hybrid uncertainty.The present method consists of a sequence of iterations.At each step,a response surface model is constructed for the limit-state function by using a quadratic polynomial and a modified axial experimental design method.An approximate hybrid reliability problem is created based on the response surface model,which is subsequently solved by an efficient decoupling approach.An updating strategy is suggested to improve the quality of the response surface and whereby ensure the reliability analysis precision.A computational procedure is then summarized for the whole iterations.Four numerical examples and also a practical application are provided to demonstrate the effectiveness of the present method.
基金co-supported by the National Natural Science Foundation of China (Nos. 51675026 and 71671009)the National Basic Research Program of China (No. 2013CB733002)
文摘The classical probabilistic reliability theory and fuzzy reliability theory cannot directly measure the uncertainty of structural reliability with uncertain variables, i.e., subjective random and fuzzy variables. In order to simultaneously satisfy the duality of randomness and subadditivity of fuzziness in the reliability problem, a new quantification method for the reliability of structures is presented based on uncertainty theory, and an uncertainty-theory-based perspective of classical Cornell reliability index is explored. In this paper, by introducing the uncertainty theory, we adopt the uncertain measure to quantify the reliability of structures for the subjective probability or fuzzy variables, instead of probabilistic and possibilistic measures. We utilize uncertain variables to uniformly represent the subjective random and fuzzy parameters, based on which we derive solutions to analyze the uncertainty reliability of structures with uncertainty distributions. Moreover, we propose the Cornell uncertainty reliability index based on the uncertain expected value and variance.Experimental results on three numerical applications demonstrate the validity of the proposed method.
