High-dimensional complex system uncertainty analysis method based on statistical machine learning

Abstract

The invention discloses a high-dimensional complex system uncertainty analysis method based on statistical machine learning, and the method comprises the steps: selecting uncertainty factors affectinga high-dimensional complex system, and obtaining a high-dimensional random variable input sample matrix; inputting the high-dimensional random variable into a sample matrix, and converting the samplematrix into a low-dimensional random variable sample matrix; inputting the high-dimensional random variables into a sample matrix for one-by-one calculation to obtain an output response quantity matrix; performing accurate modeling on the random response surface agent model to obtain a random response surface model highly approximate to the researched high-dimensional complex system; obtaining amean value and a variance of an output response quantity of the random response surface model by a formula derivation method; and analyzing the uncertainty factors according to the mean value and thevariance to obtain an uncertainty analysis result. The method has the advantages that the calculation result has high accuracy, the calculation amount is reduced and the calculation efficiency is improved on the basis of ensuring the calculation precision, the problem of dimensionality disasters is avoided, the flexibility degree is high and the like.

Description

technical field [0001] The invention relates to the technical fields of high-dimensional reduction and statistical machine learning, in particular to an uncertainty analysis method for high-dimensional complex systems based on statistical machine learning. Background technique [0002] Nowadays, due to the needs of research in various fields, there are a large number of important practical problems that urgently need to be solved by precise modeling. These practical problems often represent high-dimensional complex systems, such as: long-span bridge construction, terrestrial hydrological system modeling, Remote sensing inversion, aircraft design optimization, comprehensive energy system analysis, etc. However, almost all systems in practice have varying degrees of uncertainty and nonlinearity, which pose challenges for accurate modeling. [0003] When analyzing the uncertainty of high-dimensional complex systems, the traditional method is to set up parameters according to t...

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Problems solved by technology

[0005] What also needs to be considered is that although the obtained low-dimensional features can represent the original high-dimensional data, they will more or less miss information.

In addition, the proxy model also has requirements on the dimensionality of the input data. If the dimensionality is too low, it will lead to insufficient training and the training effect is not obvious. If the dimensionality is too high, the model will be overfitted and the model burden will be increased.

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