In which aspects has the fabric spreading machine been applied

Since only dimensional integration is involved, when the interaction of the input variables of the placing machine occurs, it will bring considerable errors. Moreover, since the integration is based only on a single variable, the method of increasing the number of integration nodes cannot be used to compensate for the errors in the interaction calculation. Therefore, this method shell is suitable for high-dimensional and low-coupling uncertain propagation computing models. The sparse grid uncertain propagation method, as a relatively special method in numerical integration methods, is mainly used to solve higher-dimensional uncertain propagation problems. Its emergence has opened up a brand-new perspective for the study of uncertain propagation. The sparse grid technology is based on algorithms as its mathematical foundation. Its basic idea is to construct a discrete sample space by using the definite combination of the product of dimensional integrals and point vectors. Compared with the tensor grid technology, the sparse grid technology, while ensuring the accuracy, reduces the number of sample points by removing the points in the tensor grid that have a smaller impact on the calculation accuracy, avoiding the increase in the amplitude of sample points caused by the increase in dimension and accuracy. At present, the superiority of sparse grid technology in dealing with high-dimensional problems has been proved and it is widely applied in fields such as numerical solution and image processing. Automatic placing machine

The uncertain propagation method based on sparse grids mainly extends the numerical integration technique of sparse grids under determination to random Spaces. Starting from the Gaussian integral form of the dimension, by adopting special tensor product operations on it, the integral in the high-dimensional case is obtained. The difference between it and the full-factor numerical integration method lies in that the full-factor numerical integration method directly adopts the direct tensor product operation on the Gaussian integral of the dimensional form, while the sparse mesh method implements a special tensor product operation by adopting algorithms. Therefore, the number of integration points generated is less than that of the full-factor numerical integration method. This is particularly evident in high-dimensional conditions. The construction of a lattice is very simple. By directly using the tensor product operation, the integration points within it can be obtained. The sparse grid requires the synthesis of several grid points larger than the direct tensor product to obtain the integral points of the sparse grid. The uncertain propagation method based on sparse grid numerical integration shows great advantages and potential when solving high-dimensional problems. Uncertain optimal design. Design problems based on uncertainty mainly fall into two categories: robust design problems and reliable design problems.