Residual-Based Modeling and Signal Decomposition in Phase-Controlled Multi-Mass Systems

This work presents a modeling and analysis framework for phase-controlled, mechanically coupled multi-mass systems under external excitation. The focus lies on the decomposition of the measured signal into physically interpretable components and residual contributions. A structured formulation is introduced in which the measured normal force is expressed as a superposition of dynamic contributions and a generalized artifact term. A residual-based approach is proposed to separate model-consistent dynamics from non-identifiable or artifact-related components. The decomposition is explicitly recognized as non-unique and dependent on model assumptions. Synthetic simulations are used to validate the internal consistency of the formulation and to demonstrate the behavior of the residual under controlled conditions. The results confirm that near-zero error levels can be achieved within the defined modeling framework, while not implying physical correctness. The scope of this work is limited to modeling, signal decomposition, and methodological analysis. No claims regarding new physical principles are made. This work builds upon the framework introduced in: Früh, M. (2026). A Pre-Experimental Framework for the Investigation of Phase-Controlled Multi-Mass Systems. Zenodo. https://doi.org/10.5281/zenodo.19372042