The method combines neural networks with polynomial interpolation or estimation techniques.
The design of aerodynamic components of aircraft, such as wings or engines, involves a process of obtaining the optimal component shape that can deliver the desired level of component performance, subject to various constraints, e.g., total weight or cost. Aerodynamic design can be formulated as an optimization problem that involves the minimization of an objective function over the design space, subject to constraints.
A method was developed for constructing composite response surfaces by combining neural networks with polynomial interpolation or estimation techniques. It combines the strengths of neural networks and other interpolation/estimation techniques by constructing composite response surfaces using parameter-based partitioning. In parameter-based partitioning, the functional dependence of the variables of interest with respect to some of the design parameters is represented using neural networks, and the functional dependence with respect to the remaining parameters is represented using other interpolation/estimation techniques, e.g., polynomial regression methods. This app - roach is an extension of traditional response surface methods that are based on polynomials alone. The use of neural networks in conjunction with other methods results in a composite response surface that models the functional behavior in design space or modeling space. When first- or second-order polynomials are used, the number of data sets required increases in a linear or quadratic manner, respectively, with the number of parameters.
Although several methods can be used to represent the functional behavior of the design data, neural networks are particularly suitable for multidimensional interpolation where the data are not structured. Since most design problems in aerodynamics involve a multitude of parameters and datasets that often lack structure, neural networks provide a level of flexibility not attainable with other methods.
In addition to drastically reducing the computational requirements to obtain the simulation data, the method of the present invention also has a dramatic impact on the neural net training process. First, the reduction in the total amount of simulation data greatly reduces the training requirements. Second, the use of multiple estimation methods to represent the data also reduces training times. This is because a part of the complexity of representing the function is transferred from the neural network to the polynomial approximation.