Volterra Series as an Intermediate Representation for Designing Smart Mechanical Structures

We have recently demonstrated speech recognition by linear passive elastic mechanical structures. However, the design of these structures requires computationally challenging non-convex optimization, which complicates inclusion of non-linear interactions in the design. Non-linear systems can be represented by Volterra series, which offer a generalization to impulse responses, under the assumption of fading memory. Since speech recognition is of fading memory, we propose to optimize mechanical systems for speech recognition through Volterra series representations. Here, we investigate how Volterra series representations can be realized through the dynamics of mechanical structures. We consider binary classification of spoken words by optimizing the Volterra kernels up to second order, and how these can be implemented by passive mechanical systems.