Research On Dimension Reduction Method Based Non-Gaussian Compound Random Vibration And Reliability

The physical properties,geometric parameters and loads of engineering structures have complex spatio-temporal variability,so the behavior of the structure is no longer deterministic,but quantitatively describes this uncertainty in the form of random field functions and time functions.Structure and structural analysis are gradually developing,and have been widely used in engineering applications.Generally speaking,it is reasonable to describe the randomness of the structure as random variables,but for most important design loads like earthquakes and wind,it is more reasonable to treat them as random processes.The problem of random processes acting on random structures is called the compound random vibration problem.Therefore,based on time-domain methods,this paper takes non-Gaussian compound random vibration as the research goal,and conducts three aspects of researches,including non-Gaussian stochastic process simulation,dimension reduction approximate and application,and non-Gaussian load based compound random vibration problem.(1)To simulate non-Gaussian stochastic process,a new stochastic harmonic function based stochastic process simulation is proposed.Non-Gaussian stochastic process simulation is the basis of the time-domain analysis method for random vibration.The non-Gaussian simulation of the traditional method is inefficient.On the one hand,even for multi-point Gaussian simulation,the superposition of too many harmonious components will consume a lot of efforts and time.On the other hand,it is necessary to obtain the potential Gaussian power spectrum,however,the "incompatible" problem and solving the correlation coefficient transformation equation are also troublesome.Based on the stochastic harmonic function,this paper develops an efficient multivariate simulation method for stochastic processes,and then uses a memoryless nonlinear transformation and Mehler equation to further develop the proposed method to multivariate non-Gaussian stochastic process simulations.(2)To enhance the efficiency of analyzing high-dimensional system,researches and application on dimension reduction methods are carried out.Compound random vibration is a typical high-dimensional problem.The dimension reduction method is essential for analyzing high-dimensional random problems.Based on the existing dimensionality dimension reduction methods,this paper firstly develops a higher-order cross-term judgment criteria and the corresponding judgments to develop a new vector-based dimension reduction method,and further to guide the application of the dimension reduction methods.Based on the dimension reduction methods of the original function,the direct integration method and the anisotropic sparse grid are developed to estimate the statistical moments,respectively;the moment-independent sensitivity analysis based on the first four-order moment and the maximum entropy are studied,and the single-and double-loop for moment-independent sensitivity analysis are discussed;a dimension reduction method aided active-learning Kriging is developed for reliability.(3)To analyze non-Gaussian load excited compound random vibration,a partial vector-based dimension reduction method is exploited.Based on the conditional random systems,decoupling random structures from loads is an effective way to solve compound random vibration.In fact,the decoupled compound random vibration problem is transformed into several random vibration problems of deterministic structure.The time-domain explicit method can obtain the response coefficient matrix of the deterministic structure through two structural analyses,which is an effective method to solve the random vibration of the deterministic structure in time domain.Based on the conditional random systems,the dynamic responses and moment-independent sensitivity of linear structures based on Gaussian and non-Gaussian load are effectively analyzed.Finally,based on the first-time transcendence probability and equivalent extreme value event,an efficient dynamic reliability method for compound random vibration is proposed.In the end,the main conclusions of this paper are briefly summarized as follows:By reducing the random harmonic terms,a more efficient non-Gaussian stochastic simulation is developed,which reduces the curse of high dimensionality compared with the traditional spectrum method.By studying the dimension reduction methods,two kinds of vector-based methods are developed,which improves the precision and broadens the scope of dimension reduction methods.Through the partial vector based dimension reduction method,a new compound random vibration moment analysis method is proposed to calculate moment-independent sensitivity and dynamic reliability efficiently.