Fractional-order elastic net regularization for identifying various types of unknown external forces

Abstract

Force identification is an important and fundamental problem in various engineering fields, and several regularization techniques have been introduced to improve the ill-posedness of this problem. While these regularization techniques can achieve satisfactory identified accuracy, they are best suited for dealing with specific forms of external forces. The external force, in reality, is always unknown and needs to be identified, making it difficult to select an appropriate regularization technique in advance. To overcome this disadvantage, a novel regularization technique, i.e. fractional-order elastic net regularization is proposed for force identification in this study. Firstly, the relationship between acceleration response and coefficient vector of external force is established. Then, a weighted matrix is introduced to define the difference between measured and calculated acceleration responses. Meanwhile, the external force and coefficient vector are constrained by their respective norm penalties with the help of regularization parameters. As a result, an optimization problem is defined for force identification, and the corresponding geometric significance is analyzed to propose a selection way for the regularization parameters. Finally, both numerical simulations and experimental verifications are conducted to evaluate the effectiveness of the proposed method. Comparison with existing methods reveals that the proposed method has great identification accuracy and applicability for various types of external forces.