The Dynamical Analysis Method And Its Application For The Multibody System With Uncertain Parameters

There exists a large amount of uncertain parameters in engineering.It has become an important project to evaluate the influence of the uncertain parameters on the dynamical behavior for the reliability and robustness of a system.The response surface method,as a common uncertainty analysis method,suffers from a problem that its accuracy decays with the increase of time,when dealing with the periodic time-dependent response.In the design of a liquid rocket,it is critical for engineers to understand how the uncertain parameters affect the rocket's response.For the two problems,this thesis carries out the following three studies:A new uncertainty analysis method by combining response surface method with signal decomposition technique is proposed.Studying the time-dependent response under the uncertain parameters,the conventional response surface method works by building a polynomial surrogate model at each time instant through a set of input and corresponding output responses.However,with the increase of time,a dynamic response always becomes a more and more complicated function with respect to uncertainty parameters;as a result,the fitted surrogate model often fails to provide an accurate approximation at later time instants.This thesis reveals that a dynamic response is composed of several vibration components and one trend component.Therefore,it is better to decompose the response into its multiple components,and then fit the amplitude and phase of each vibration component,as well as the trend component,using polynomial functions,than to build surrogate model directly for the response itself.By combining the response surface method with signal decomposition techniques,such as Hilbert-Huang transform and local mean decomposition,this thesis proposes a novel methodology to develop a highaccuracy surrogate model for interval uncertainty analysis.The proposed methodology greatly improves the accuracy of the surrogate model of the conventional response surface method,and significantly decreases the required sample numbers.This methodology provides a new technical pathway for the dynamical uncertainty analysis.A new uncertainty analysis method by combining response surface method with hierarchical signal decomposition technique is proposed.Except that a response itself contains several harmonic waves,the amplitude and phase of the response might also have their own structure that contains several harmonic waves.So,when dealing with a nonlinear response,there always exists some error in the surrogate model of the uncertainty analysis method combining the response surface method with the single-level signal decomposition technique.To reduce the error,the amplitude or the phase can be further decomposed to obtain the second-level decomposition result.Then,the surrogate models are built for the amplitude,phase and trend of the first-level and second-level decomposition results.As a result,a nested surrogate model composed of two sub-surrogate models is formed.Therefore,this thesis proposes a new uncertainty analysis method by combining the response surface method with hierarchical signal decomposition technique,such as hierarchical Hilbert-Huang transform and hierarchical local mean decomposition.The proposed method can improve the accuracy of the surrogate model without increasing the number of samples,and clearly reveal how the uncertain parameters affect the system's response.The effect of the uncertain parameters on the dynamics of the liquid rocket is revealed.The locally weak nonlinearity and weak coupling of the uncertain parameters on the load of the liquid rocket is found.The low-order response surface method is used to analyze the effect of 20 uncertain parameters on the load of the rocket.The five parameters(i.e.,the thrust,the mass of propellant,the dynamic head,the lateral coefficient and the lift coefficient)that have a significant effect on the load are selected among the 20 uncertain parameters.The estimated value 1.3 of the safety factor is obtained.The results of the uncertainty analysis can provide a reference for the rocket design.