Downhole operational modal analysis

A method for selecting drilling parameters for drilling a borehole penetrating the earth with a drill string, the method comprising:

• measuring vibration-related amplitudes of the drill string during operation using one or more vibrations sensor to provide amplitude measurements;
• determining with a downhole processor one or more modal properties comprising one or more eigenfrequencies of the drill string using the amplitude measurements, the determination being made by without regard to any excitation force in a model of the drillstring;
• and
• selecting drilling parameters that apply an excitation force at a frequency that avoids a selected range of frequencies that bound the one or more eigenfrequencies using the processor.

A method for selecting drilling parameters for drilling a borehole penetrating the earth with a drill string, the method comprising:

• constructing a mathematical model of the drill string comprising dimensions and mass distribution of the drill string;
• forming a mathematical model of the drill string that includes any excitation stimulus being included as noise;
• measuring amplitudes of vibrations of the drill string due to the applied excitation forces using the plurality of vibration sensors to provide amplitude measurements;
• determining with a downhole processor one or more modal properties comprising one or more eigenfrequencies of the drill string using the amplitude measurements and the mathematical model;
• selecting drilling parameters that apply an excitation force at a frequency that avoids a selected range of frequencies that bound the one or more eigenfrequencies using the processor;
• and
• transmitting the selected drilling parameters to a drill string controller configured to control the drill string in accordance with the selected drilling parameters.