Advanced Diagnostics and Prognostics through Linear-in-the-Harmonics System Optimization (Identification)

Many diagnostics-focused artificial intelligence techniques in the state-of-the-art rely on combinations of least-squares-based autoregressive models and neural-network-like approaches. Prognostics algorithms can be built on top of the magic numbers generated from their result, but these magic numbers have limited physics-based meaning and a sampling of the system’s behavior in each of the multitude of failed states is likely necessary. In contrast, if a system identification algorithm could accurately generate measures of the parameters of the system’s physics (e.g. stiffness, capacitance, inductance), then the challenge of both diagnostics and prognostics reduces to tracking these measures against thresholds specified by the system’s engineer. In this work, the author proposes a least-squares technique paralleling the linear-in-the-parameters least-square formulation but with adaptations for the realities of the frequency domain which we expose by reviewing the intuition of Fourier’s seminal approach (scarcely shared). This work puts the new technique at odds with the incumbent autoregressive model and suggests that it can be extended beyond system identification to systems optimization possibly to solve such problems as computing optimal control-law parameters. It resonates with digital twin initiatives by providing one further factor to improve the economies of scale of the effort of systems physics modelling. Beyond diagnostics and prognostics, as a generalized approach to systems optimization, the new algorithm could provide a new formulation of model predictive control.