Research On Computational Uncertain Inverse Methods Based On Interval

Due to the influences of the complexity of structure,the finiteness of experimental conditions,the difference of cognitive ability,the inaccuracy of measurement data and other factors,the uncertainty inverse problem commonly exists in practical engineering,such as load identification,crack recognition and material characteristic parameter estimation etc.Although uncertainty is sometimes very small,it will also lead to larger errors in identified parameters or response spaces.Thus,the study of effective uncertainty computation inverse method is beneficial to the accurate evaluation of identified uncertain parameters.The method based on probability to measure uncertainty is the most commonly used method,but constructing accurate probability density function usually requires a large number of samples.With regard to complex engineering problems,it is easier to get the upper and lower bounds of uncertain parameters.Therefore,the inverse method based on interval is an important method to deal with the uncertainty inverse problem.For interval uncertainty inverse problem,it is generally translated into a two-layer solution of uncertainty propagation and model parameter optimization.Most of the traditional methods are based on the first order Taylor expansion to deal with the uncertainty propagation problem in the inner layer.However,the method based on the first order Taylor expansion is not suitable for interval inverse problems with high er nonlinearity and larger uncertainty.In order to solve this kind of interval uncertainty inverse problem better,this paper constructs a model of interval uncertainty inverse,studies the interval calculation inverse method based on high dimensional model representation and affine arithmetic and the interval calculation inverse method based on DIRECT algorithm.The following three aspects are the main research contents of this article:(1)The optimization model of interval uncertainty inverse is constructed.In order to describe the approximation degree between computing response interval and measurement response interval,an error interval is proposed.According to the error interval,an optimization model for interval uncertainty inversion is established,so that the calculation inverse problem of interval is transformed into optimization problem.(2)For the inverse problem of interval uncertainty with higher nonlinearity,a calculation inverse method of interval uncertainty based on high dimensional model representation and affine arithmetic is proposed.Firstly,in order to simplify the original complex system model,the high dimensional model representation is used to approximate the original system model,and the original high dimensional system model is transformed into a combination of m ultiple low dimensional subentries.Secondly,in order to reduce the expansion error in interval propagation,affine algorithm is utilized to get the interval of computation response.Finally,genetic algorithm is applied to solve the optimization problem with respect to the interval uncertainty inverse,and the interval of identified parameters can be obtained.(3)In order to further improve the accuracy of interval uncertainty inverse,an interval uncertainty computation method based on DIRECT algorithm is proposed.Firstly,the DIRECT algorithm is used to get the range of computation response more efficiently,and it further reduces the error in the interval propagation process.Secondly,in order to reduce the number of invocation of the original system model,an adaptive radial basis function surrogate model is built to approximate the original time-consuming system model.Finally,genetic algorithm is utilized to solve the optimization problem of interval uncertainty inverse,and the interval of identified parameters is obtained.