Virtual Emulation of Power Meters in Indoor Cycling: A Robust Hybrid Linear Regression Model for the Democratisation of Performance Metrics

Abstract

Background: Mechanical power output (W) constitutes the reference variable for quantifying external load in cycling. Nevertheless, the economic and logistical constraints associated with strain-gauge power meters continue to limit their adoption to elite or well-resourced populations [1–5]. Purpose: This study aimed to develop and validate a virtual instrumentation approach—a Hybrid Linear Regression Model (HLRM)—capable of estimating cycling power using readily available physiological and anthropometric inputs, thereby emulating physical power meters through computational means. Methods: Sixteen regular indoor cyclists (12 women and 4 men; age range: 38–84 years) completed progressive ramp protocols on a calibrated cycle ergometer equipped with a direct-force power meter [14,15]. A total of 192 validated effort-zone observations were collected at a fixed cadence of 80 RPM. Model development followed a hybrid strategy: an initial ordinary least squares (OLS) formulation was refined using Huber robust regression to attenuate the influence of physiological outliers [9,21,22]. Fractional heart-rate effort and quadratic non-linear terms were incorporated to reflect established curvilinear relationships between effort and power [10–13,18]. A secondary robust submodel was implemented to estimate individual power threshold in the absence of laboratory testing. Results: The initial complete OLS model exhibited substantial multicollinearity (variance inflation factor > 5) and physiologically inconsistent coefficients. The optimised HLRM (SpinPower Pro) resolved these issues, yielding a coefficient of determination R^2=0.952, a mean absolute error (MAE) of ±4.8 W, and a root mean square error (RMSE) of 5.3 W. Validation using exemplar reserve cases demonstrated robust generalisation across markedly different anthropometric profiles, with residual errors remaining below 8 W, a performance comparable to validated commercial power meters [1,4,24–26,30,39,40]. Conclusions: The proposed hybrid model emulates direct power measurement with an accuracy comparable to entry-level hardware power meters. By integrating robust statistical techniques with physiologically informed heuristics, this approach enables smartphones and standard wearable sensors to function as virtual scientific instruments, substantially reducing barriers to power-based training.