Non-destructive early detection of water stress is critical for precision agriculture, yet current detection methods are often labor-intensive or destructive. We propose a rapid, non-invasive method based on Spectral Submanifold (SSM) reduction to analyze the nonlinear vibration dynamics of soybean plants. Unlike traditional linear modal analysis, our data-driven approach reveals a distinct transition in the dominant dynamics of the plant stem as drought progresses. Specifically, we uncover a sign reversal in the nonlinear damping coefficient within SSM-reduced models of full plants. Our finding reveals a fundamental transition in the plant's dissipative mechanics from a pressurized, fluid-rich vessel exhibiting superlinear (viscoelastic) damping to a dry, cellular solid dominated by sublinear (frictional) damping. This transition is closely correlated with the onset of physiological stress indicated by a significant decrease in the values of mature-leaf soil plant analysis development (SPAD) and colorimetric metrics. In contrast, traditional metrics, such as linear frequency and leaf wilting, do not provide consistent statistical signals of water stress. This study provides the first experimental evidence that SSM-based nonlinear model reduction can detect the changing internal state of a living organism, offering a physics-based metric for high-throughput plant phenotyping.
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