Application of machine learning procedures for mechanical system modelling: capabilities and caveats to prediction-accuracy

Abstract

This article presents an investigation about prediction accuracy of multi-parametric models derived from numerical data. Three different mechanical test-cases are used for the generation of the numerical data. From this data, models are derived for the prediction of characteristic variation to arbitrary changes of the input parameters. Different modeling approaches are evaluated regarding their prediction accuracy. Polynomial matrix equations are compared to regression models and neural network models provided by Machine-Learning toolboxes. Similarities and differences of the models are worked out. An exponential matrix-equation-model is proposed to increase accuracy for certain applications. Influences and their causes to the prediction accuracy for the model predictions are evaluated. From this minimum requirements for deriving valuable models are defined. Leading to a comparison of the modelling approaches in relation to physical plausibility and model efficiency. Where efficiency is related to the effort for data creation and training-procedure. For one of the sample cases, a prediction-model is applied to demonstrate the model application and capabilities. The model equation is used to calculate the value of a penalty function in a multi-input/multi-output optimization task. As outcome of the optimization, four natural frequencies are fitted to measured values by updating material parameters. For all other cases sensitivity-studies including verification to numerical results are conducted.