A Class Convex Optimization Method Of Uncertainty Information Quantification And Application In Compressed Sensing

With the increasingly high demand for system reliability,the effects of random factors which exist widely in complex modern engineering systems on the whole system reliability can't be ignored.The study of the random factors has more than a century,the early researches main using stochastic programming approach to model random factors.However,most of them required that the form of probability measure which includes was highly special.Therefore,it was difficult to further popularization and application because of the very high computation complexity to solve this kind of stochastic programming problems.So many following scholars put forward to robust optimization which described uncertainty factors via set and distributionally robust optimization which combined stochastic programming with the traditional robust optimization.Robust optimization was often too conservative,and unable to use the distribution information of uncertain parameters.Distributionally robust optimization obtained its accurate solution tend to be NP-hard under the condition that only the first order moment and second order moments of the probability distribution known.Due to the existing problems in above methods,American scholar Houman Owhadi put forward a scalable and based on moment information ideological framework,namely the convex optimal uncertainty quantification,which can estimate the optimal value of objective function under the condition that only the partial statistical distribution information of the uncertainty parameters known.This paper carries on some researches in the algorithm and application based on the ideological framework,the main researches as follows:1)Based on the reading to related literatures,combining with research background and significance of uncertainty information quantification,the current research status are induction and summarized,and the theoretical basis with successful engineering applications of uncertainty information quantification framework are analyzed in deep,the existing challenging problems are induced.2)For the existing accurate solving method requires much computation time,and the approximate calculation method needs run the same optimization problem many times with different initial conditions to get the reliable optimal value,the event-driven approximate solving method is proposed.This method decided whether the event happen based on the information contribution size of previous and next constraints,need not run many times and more stable and reliable.3)A new signal recovery method in compressed sensing based on convex optimal uncertainty quantification is proposed,which takes advantage of the statistical distribution information of noises in measure signals,overcomes the problem that the statistical information of noises can't be used and need to view it as bounded constraints.