Views: 1 Author: truemax Publish Time: 2022-02-26 Origin: truemax
However,since only dimensional integration is involved,when the interaction between the input variables of the placing machine is very large,it will bring relatively large errors,and since the integration is only based on a single variable,it cannot be used by increasing the number of integration nodes to make up for the mutual calculation of the placing machine.Therefore,this method shell is suitable for high-dimensional and low-coupling uncertainty propagation calculation modes.The sparse grid uncertainty propagation method is a special method in the numerical integration method.The sparse grid uncertainty propagation method is mainly used to solve the problem.Higher-dimensional uncertainty propagation problems.Its emergence opens a new horizon for the study of uncertainty propagation.The sparse grid technology is based on the algorithm,and its basic idea is to use the definite combination of the dimensional integral point-vector product to construct a discrete sample space.Compared with the tensor grid technology,the sparse grid technology ensures the accuracy,and reduces the number of sample points by removing the points in the tensor grid that have little influence on the calculation accuracy,avoiding the increase of dimension and accuracy.The resulting increase in the number of sample points.At present,the superiority of sparse grid technology in dealing with high-dimensional problems has been proved,and it is widely used in numerical solution,image processing and other fields.
The uncertainty propagation method based on sparse grid mainly extends the deterministic sparse grid numerical integration technique to random space.Starting from the dimensional Gaussian integral form,by taking a special tensor product operation on it,the integral in the high-dimensional case is obtained.The difference between it and the full-factor numerical integration method is that the full-factor numerical integration method directly adopts a direct tensor product operation on the Gaussian integral in the dimension form,while the sparse grid method implements a special tensor product operation by using an algorithm.Compared with the full factor numerical integration method,the number of integration points is reduced.This is especially noticeable in the cloth machine,especially in high dimensional conditions.The construction of the middle lattice is very simple,and the integral point can be obtained by directly using the tensor product operation.The sparse grid needs to integrate several grid points that depend on the direct tensor product to obtain sparse grid integration points.The uncertainty propagation method based on sparse grid numerical integration shows great advantages and potential in solving high-dimensional problems.Uncertain Optimal Design Uncertainty-based design problems are mainly divided into two categories:robust design problems and reliable design problems.
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