Frequency domain work analysis of machinery including turbomachinery

A machine comprising:

• a motor rotationally coupled to a load;
• a sensor configured to measure input power electrical current supplied to the motor;
• and
• a controller in electrical communication with the motor and the sensor, the controller configured to:
• (i) operate the motor at a plurality of speeds within a range bounded by a lower speed and an upper speed;
• (ii) receive, from the sensor, a current measurement at each of the plurality of speeds;
• (iii) correlate each current measurement to its corresponding speed to generate correlated speed-current data;
• (iv) determine, from the correlated speed-current data, a plurality of numerically calculated derivatives of current with respect to speed;
• (v) determine, from the plurality of numerically calculated derivatives of current, a plurality of derived values of coefficients A and B that fit the correlated speed-current data to a model, having at least two terms, of the form A·ωn1+B·ωn2, the model representing a load-dependent relationship between current and speed, where ω is the speed and n1 and n2 are real numbers individually selected from the group consisting of 0, 1, 2, 3, and k (k being a non-integer real number);
• (vi) identify a speed at which at least one of the determined coefficients A or B satisfies a predetermined criterion;
• and
• (vii) operate the motor at a speed determined based on the identified speed.