Interval uncertainty optimization method based on BP neural network differentiation and interval analysis

Abstract

The invention discloses an interval uncertainty optimization method based on BP neural network differentiation and interval analysis. The interval uncertainty optimization method comprises the steps of training a BP neural network agent model of an original model; employing NSGA-II algorithm in an outer-layer optimization solver, calculating an inner layer interval by adopting an interval analysismethod; for each group of design variables, carrying out interval division by adopting a sub-interval technology; inputting the interval median of the subinterval combination into a neural network tocalculate an output response, carrying out a neural network first-order differential operation, carrying out first-order Taylor series expansion on the uncertainty objective function and the constraint function, and calculating the intervals by adopting an interval expansion method and an interval set method; converting the uncertainty optimization model into a multi-objective determinacy optimization model through an interval sequence, an interval possibility and an error economy evaluation index; and using NSGA-II algorithm for performing simulation search to obtain a Pareto optimal solution set. Through the method, the nonlinear interval uncertainty optimization problem, especially the engineering uncertainty optimization problem, can be efficiently solved, and the method has high engineering practical value.

Description

technical field [0001] The invention relates to structure optimization technology, in particular to an interval uncertainty optimization method based on BP neural network differentiation and interval analysis. Background technique [0002] Considering the influence of various uncertain factors such as material properties, dimensional tolerances, and loading conditions, the performance function of an actual engineering system must be uncertain. Using traditional deterministic optimization methods that ignore these uncertain factors, the optimal solution obtained is often an infeasible solution that violates constraints. Therefore, in the modeling of optimization problems, uncertain factors need to be considered to obtain solutions that are more suitable for engineering practice. [0003] The interval programming method has been widely used in uncertain optimization because it only needs upper and lower bounds of uncertain parameters and does not need other information. For ...

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Problems solved by technology

Compared with the original simulation model, the surrogate model improves the optimization efficiency to a certain extent, but the nested optimization cost of using the surrogate model is still unacceptable

The other is an uncertain optimization method based on interval analysis. This method is effective for situations where numerical differentiation is easy to solve. However, for engineering problems without explicit functional relations, a large number of original simulation models need to be called during the optimization process. would incur huge computational costs

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