Abstract: There are two famous function decomposition methods in math: the Taylor series and the Fourier series. The Fourier series developed into the Fourier spectrum, which was applied to signal decomposition and analysis. However, because the Taylor series function cannot be solved without a definite functional expression, it has rarely been used in engineering. We developed a Taylor series using our proposed dendrite net (DD), constructed a relation spectrum, and applied it to decomposition and analysis of models and systems. Specifically, knowledge of the intuitive link between muscle activity and finger movement is vital for the design of commercial prosthetic hands that do not need user pre-training. However, this link has yet to be understood due to the complexity of the human hand. In this study, the relation spectrum was applied to analyze the muscle–finger system. One single muscle actuates multiple fingers, or multiple muscles actuate one single finger simultaneously. Thus, the research was focused on muscle synergy and muscle coupling for the hand. The main contributions are twofold: (1) The findings concerning the hand contribute to the design of prosthetic hands; (2) The relation spectrum makes the online model human-readable, which unifies online performance and offline results. Code is available at https://github.com/liugang1234567/Gang-neuron.

Key words: Taylor series; Relation spectrum; Dendrite net (DD); Prosthetic hands; Machine learning; Engineering

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