The Recovery Of Random Fields Based On Incomplete Probabilistic Information

In practical engineering problems,the random fields are often unable to obtain their complete probability information due to practical reasons,but only partial observation and probability information.Due to the high efficiency and simplicity of Karhunen-Loève(K-L)expansion and the orthogonal characteristics of Polynomial Chaos(PC)expansion,they have become two important methods for the simulation of random field.Based on these two expansion methods,this paper recovers the random field with incomplete probability information with higher accuracy,and proposes a new random field simulation framework.The two core issues of this framework are the description of K-L random variables and the form of PC expansion.This paper uses these as starting points to propose three random field simulation methods and verifies the accuracy and efficiency of each method.A random field recovery method based on independent random variables polynomial chaos is proposed.In the form of K-L expansion for random field,K-L random variables are processed by independent means.And the obtained independent random variables are expanded by polynomial chaos.The random response of the system is analyzed.A random field recovery method based on dependent random variables polynomial chaos is proposed.The K-L expansion expression form of the random field is not processed independently,and the dependent K-L random variables are directly used to construct the multi-dimensional K-L random variables’ probability density function.Multi-dimensional samples are sampled from the probability density function to realize the simulation of the random field,and the multi-dimensional dependent orthogonal polynomials in the form of tensor product to efficiently express the output random field.A random field recovery method based on the B-spline maximum entropy is proposed.On the basis of the independent expression of the random field K-L expansion,the B-spline maximum entropy method is used to estimate the probability density of each independent random variable,and multi-dimensional orthogonal polynomials in the form of a tensor product are constructed.The random field simulation is realized by sampling in the maximum entropy density function.Efficiently express the output random field in the form of polynomial chaos expansions.Through the comparison with the original random field and the random field assumed by the independence of K-L random variables,the accuracy of the above three methods in the recovery of the random field and the robustness and convergence efficiency of the uncertainty propagation are verified,thus explaining the practicality of the random field simulation framework.