Phase-Sensitive Validation of Reduced-Order Nonlinear Mechanical Models with Dynamic Readout

Abstract

Reduced-order models of nonlinear structures are often evaluated using mechanical response errors, while the signals of interest may also pass through dynamic readout channels that modify their amplitudes and phases. We develop an offline validation framework that distinguishes mechanical source error, readout-model prediction error, and physical distortion of a normalized two-component modal state. We couple a Galerkin reduced source to two calibrated resonant channels and evaluate modal amplitudes, relative phase, and state fidelity using consistent complex coefficients. For the linear readout model, an exact output-error decomposition distinguishes source and interface modeling contributions, while a two-channel identity relates differential channel transfer to normalized-state distortion. For the ten-mass nonlinear lattice, the two-mode source and coupled-output errors over the two-resonance interface band are $3.069 \times 10^{-2}$ and $2.448 \times 10^{-2}$. At $F_0=0.04$, the relative-phase mean absolute error increases from $9.82 \times 10^{-3}$ rad for the linear interface to $1.74 \times 10^{-2}$ rad for the nonlinear interface. At the strongest forcing, a four-coordinate proper orthogonal decomposition model gives a source error of $2.05 \times 10^{-2}$, compared with $8.03 \times 10^{-2}$ for four linear modes on the same held-out test set. The noise analysis shows that accurate in-band output prediction can coexist with substantial parameter error, while a constrained linear approximation of nonlinear readout data produces a substantial residual. We use these findings to assess reduced-model adequacy for the specified outputs, forcing levels, and validation frequencies.