A method for selecting drilling parameters for drilling a borehole penetrating the earth with a drill string. The method includes: 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 including any excitation force in a white noise term of 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.