GA-BP neural network-based nonlinear regression model for machining errors of compressor blades

Given that blade machining errors can substantially degrade aeroengine performance and reliability, there is a critical imperative to implement stringent control over blade machining errors during the manufacturing process. Nevertheless, the prevailing complexity surrounding the numerous machining error types and their obfuscated interrelationships impedes the comprehensive control of blade profile errors. Consequently, unveiling the nonlinear relationships between the distinct machining errors represents a task of paramount importance. To uncover these nonlinear relationships, this work pioneers the application of factor analysis and Genetic Algorithm-optimized BP neural networks to enable nonlinear regression for diverse blade machining errors. Specifically, this paper first constructs an orthogonal factor analysis model to reduce the dimensionality of complex, high-dimensional blade machining error data and extract underlying correlations. This analysis reveals three distinct error groups, each dominated by a latent common factor. Building on these factor analysis outputs, GA-BP neural networks are then leveraged to perform nonlinear regression for intra-group errors. Guided by the Maximal Information Coefficients (MIC) between different errors, we identify control error types within each group to serve as network inputs, with other errors designated as outputs. To prevent overfitting and accelerate convergence of the neural network, Monte Carlo method is used to augment the limited raw error dataset. The augmented data trains the GA-BP network, establishing multivariate nonlinear models with control errors as independent variables and other errors as dependent variables. The model accuracy is validated by a separate validation set. The comparisons between the predicted and true values in the validation set reveal that the relative errors are around 5%, indicating that the models achieve an accuracy of approximately 95%. These results demonstrate the satisfactory performance of the established models. Overall, this work elucidates previously unclear relationships between distinct blade machining errors. These new insights establish the foundation for comprehensive error control and will directly benefit blade design, manufacturing, and performance.