# Concluding Remarks

A broad range of techniques are presented in this chapter. The varying methods will be useful in different circumstances and hence there is no golden rule on which approach to use when. The suitability will depend on the type of data and the features to be extracted.

# Problems

- 8.1 A uniform steel rotor, 1 m in length, is supported at each end on bearings, each of which has constant stiffness 5х10
^{э}N/m with damping od 150 Nsec/m . There are two discs mounted 250 mm from either end and both of these are steel with thickness 20 mm and diameter 100 mm. The first disc has an imbalance of 0.04 kg mm, while the second has an imbalance of 0.02 kg mm, both at zero phase. The shaft passes through a clearance of 10pm at midspan. Calculate the response and determine the speed at which the shaft will contact the stator. - 8.2 A time signal has the form

Determine the maximum instantaneous frequency and velocity, and the time at which these occur.

8.3 A vibration trace has the form

The white noise has amplitude of 10. Determine the autocorrelation function and identify the main frequencies.

8.4 A time-limited signal has the form

For 0

Determine an empirical mode decomposition for this signal. (Note this may be achieved either manually or with freely available MATLAB routines.)

8.5 Taking the matrix

determine the SVD of both *U* and its transpose and explain the relationship between the two.

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