The measured vibro-acoustics signatures readily depict distinct rumble characteristics in several primary sets of constant (speed-invariant) frequency ranges when
computed in a spectrogram form by employing the short-time Fast Fourier Transform approach. This is accomplished by digitizing the time domain data using an advanced signal processing system. Fig 3a and b show the spectrogram functions of engine compartment noise for no-load snap and second gear acceleration conditions, respectively. Here in Fig. 3a, one can easily see three bands of constant frequency ranges that are filled with periodically spaced intense vertical strips occurring
over a span of approximately 1 s, even though engine rotational speed is cyclical
(not constant). Similar bands can be found in the second gear acceleration data, but
they are not as clear due to the masking effect from higher engine noise. Therefore,
subsequent analysis and discussion will focus mainly on the no load snap condition.
Fig. 4 shows a comparison of a pair of spectrogram functions computed from the
firewall structure vibration data of the quiet and noisy vehicles. It can be seen that
the intensity of rumble strips in the spectrogram of the noisy vehicle is clearly more intense than the quiet one. These strips are in fact responsible for rumble sensation
and they actually intensified during each ramp-up period due to the increase in
engine load. Hence, we conclude that the phenomenon is not driven solely by combustion, but is also controlled by the structural dynamic characteristics of certain
engine components. Each strip is comprised of clusters of nearly equal amplitude,
narrow-band frequency response peaks that are either half or one order apart, which
essentially create the sensation of rumble as discovered in a series comparative listening sessions of playback filtered noise signals. As expected, the perceived quality
and relative intensity of rumble at each specific frequency band is dependent on the
precise measurement locations as implicated by the spectrogram results of Figs. 3-5
due to the geometrical complexity of the vehicle systems. This explains the dependency of previous subjective evaluation results on specific passenger positions. In
addition, the noise signatures from the microphones placed in the engine compartment and passenger cabin showed some differences in the relative strength of the
frequency content, which is an indication of the selectivity and effectiveness of the
body structure in transmitting vibratory energy within specific frequency bands.
The rumble signatures also contain significant presence of amplitude modulations,
which account for much of the perceived temporal-dependent harshness sensation of
rumble. Its amplitude modulation period or frequency is computed using three different methods as summarized in Fig. 6. The first method utilizes a band pass filter
to extract signal contents that fall within 875-950 Hz. The filtered data is A-weighted and processed to give the band-limited overall level as a function of time. A typical result is shown in Fig. 7. Here the temporal spacing intervals between consecutive peaks define the period of modulation. Since the instantaneous engine
rotational speed is known at each time point, the computed modulation period can
be related precisely to the magnitude of engine rpm. The second method involves
calculating the moving average of the specific loudness of Bark 8 corresponding to
the time-varying loudness scheme proposed by Zwicker [9,10] The result is a function of consecutive temporal peaks with intervals corresponding to the modulation
period as illustrated in Fig. 8, which can also be related to the engine speed. The
third method is rather qualitative and is simply based on extracting the time difference between adjacent rumble strips from the spectrogram function. This is the least accurate of the three methods proposed whereas the first two approaches give fairly comparable results.
Using the bandpass filter method, the periodicity of a large sample of measured
no-load snap data is computed and compared to the corresponding engine rpm as
shown in Fig. 9. Apart from the scatter in the data due to numerical calculation
error and the presence of some degree of randomness in the process, the average
trend shows a linear correlation between rumble frequency fR and engine rpm NE.