Research Of Moment-independent Importance Measure And Its Application In Optimization

In engineering practice, such as aviation industry and mechanical engineering, there are various uncertainties in the properties of material, geometry of systems and applied loads. Studying the effects of these uncertainties on the output performance of the structures is of great significance for predicting the structural behavior and developing reasonable risk evaluation and reliability model. This paper, therefore, develops the theory of global importance analysis in the presence of various uncertainties, which can provide useful information for the engineering design and optimization. The detailed contents and innovations are listed as follows:(1) In order to deal with computational efficiency of the moment-independent importance measure on the failure probability, we make full use of the advantages of both the point estimate and Line Sampling(LS) methods and develop a layered algorithm.(2) To fully analyze the effects of input variables on failure probability in structure, an extended moment-independent importance measure based on the traditional moment-independent one is proposed. The computational cost of the moment-independent important measure is too high as direct Monte Carlo simulation is used. To overcome the difficulty, an integral solution is established by combining the highly efficient and exact Kernel density estimation.(3) For structure system with fuzzy input variables as well as random ones, the importance measure analysis based on failure probability plays a great role in predication and optimization. With this respect, based on isentropic principle which transforms membership function into probability density function, a moment-independent importance measure is presented for measuring the effect of fuzzy and random variables on the reliability of the structure. For the problem of large computational cost by numerical simulation, the Kriging model is employed to represent the limit state function of the structure system and propose an efficient method is proposed to approximate the importance measure.(4) In order to improve the efficiency of engineering optimization, the theory of moment-independent importance measure is introduced here to analyze the effect of the input variables on the output response, on which an efficient optimization strategy is developed. The strategy transforms a high-dimensional engineering optimization into several optimization problems with decreased dimensionality. Thereby, the computational cost can be decreased tremendously. Then, the optimization strategy is applied into the design of high-altitude long endurance aerofoil.