ML//applied ML//physics-based features

A physics-based feature is an input to a learned model computed from raw measurements with a known physical law, so that it already discounts a dependency the engineer understands (speed, load, ambient temperature), and it is used to make a model invariant to the operating point, smaller, easier to explain and cheaper in data. Fed vibration and speed separately, a model must discover alone that one depends on the other, which takes examples at every speed with and without the fault; a feature that removes the dependency saves it from learning what the engineer already knew. (It is an input built by hand, distinct from the feature of a neural network, a direction in its activations.)

A physics-based feature is an input to a learned model computed from raw measurements with a known physical law, so that it already discounts a dependency the engineer understands (speed, load, ambient temperature), and it is used to make a model invariant to the operating point, smaller, easier to explain and cheaper in data. Fed vibration and speed separately, a model must discover alone that one depends on the other, which takes examples at every speed with and without the fault; a feature that removes the dependency saves it from learning what the engineer already knew. (It is an input built by hand, distinct from the feature of a neural network, a direction in its activations.)

The standard example is a variable-speed centrifugal pump. By the affinity laws, on an unchanged circuit the absorbed power scales with the cube of the speed, so the model receives the power referred to a reference speed:

P~=P(nrefn)3\tilde P = P\left(\frac{n_{\text{ref}}}{n}\right)^{3}P~=P(nnref​​)3

Here PPP is the measured power, nnn the current speed in rpm and nrefn_{\text{ref}}nref​ a reference speed. For a healthy pump on the same circuit P~\tilde PP~ stays nearly constant whatever the speed; when it rises, something rubs or clogs, and a model trained on it generalizes to speeds it never saw.

A feature with physics brings invariances the model no longer has to learn, and sometimes it turns the model into a threshold.

Once P~\tilde PP~ is found, a threshold on it with a little hysteresis may do the whole job, maintained by the technician on shift. That is the best possible outcome of an ML project; the model is kept for boundaries that depend on several features at once in ways nobody can write.

Bearings get the energy of the envelope spectrum at the defect frequency, expressed in orders of the shaft speed, so a fault keeps its place in the spectrum when the speed changes.

Motors get the Joule-loss normalized temperature rise, the winding temperature above ambient divided by the square of the current, ΔT/I2\Delta T/I^{2}ΔT/I2, because Joule heating grows with I2I^{2}I2. A drift in it points at cooling or insulation, whatever the load.

On rotating machines, good vibration features with gradient boosting on top usually compete head to head with deep networks on the raw signal, need far less data and are maintained with much less effort (applied ML). The same knowledge enters tree models as monotonic constraints and networks as augmentation that respects physics (data augmentation).