Technical Report: What is Fluctuation Sound Analysis 1

Sound quality evaluation metrics, including loudness, are currently widely used as a technology to quantify human auditory impressions across various fields. Recently, there has been an increase in discussions about timbre evaluation and unwanted sound detection due to time-varying components. Common indicators for detecting these include roughness and fluctuation strength, but both are metrics that only extract specific time-varying components. However, the mechanical noise emitted from industrial products often includes various fluctuation cycles, making it insufficient to extract their characteristic features. Therefore, by using a metric that can quantify various time-varying components based on loudness (fluctuation sound analysis), it becomes possible to quantify not only the timbre (pitch) of sounds but also their time-varying cycles.

Although the volume of sound is not particularly loud, there are many "annoying sounds" in the world. For example, sounds emitted by interior parts that can occasionally be heard while a car is running, such as "clattering" and "buzzing," or the abnormal sound "zi" mixed with the rotation sound of a small motor can be cited. There are several causes for what is considered "annoying," but sounds with significant temporal fluctuations often feel unpleasant even if their volume (level) is not very high.

Fluctuating sound analysis is an analysis that can extract only the large components of temporal fluctuations that are not affected by level. This allows for the quantification of various temporal fluctuation characteristics that were difficult to detect with conventional FFT, basic roughness, and fluctuation intensity. Additionally, it enables deeper analysis than conventional techniques by evaluating various sound designs (seasoning) on two axes: sound timbre (pitch) and temporal fluctuation period.

The unit of fluctuating sound analysis (DLF) stands for Depth of Loudness Fluctuation, which refers to the depth (difference) of the peaks and valleys of loudness temporal fluctuations. The graph of the analysis results is expressed in mDLF, which means it is actually a value multiplied by 1000. The (s) after DLF represents linear display, while (p) represents logarithmic display. (s is derived from the initial of the loudness unit sone, and p is derived from the initial of the loudness level unit phon.)

The basic fluctuation sound analysis indicators, Roughness, which can express the roughness of sound, and Fluctuation Strength, which can express the wavering sensation of sound, are parameters that can extract the temporal fluctuation components of sound. These parameters each have limitations on the fluctuation frequencies they can evaluate. For example, Roughness, which evaluates the roughness of sound, peaks at a fluctuation frequency of 70 Hz, with lower weighting for frequencies before and after this peak. On the other hand, Fluctuation Strength, which evaluates the wavering sensation of sound, peaks at a fluctuation period of 4 Hz, and its sensitivity decreases for fluctuation frequencies that are further away. Therefore, when considering sound fluctuations broadly, it can be said that each parameter has its strengths and weaknesses.

Fluctuation sound analysis is a parameter that can handle a wide range of fluctuation frequencies.
In contrast to the above, where a single fluctuation frequency filter is used to give sensitivity to specific frequencies for roughness and fluctuation intensity, fluctuation sound analysis employs multiple filters.
Details will be described in the next chapter (Fluctuation Sound Analysis Algorithm), but it is possible to pass through one band-limiting filter at a time from low band to high band to extract fluctuation components more finely.

I will explain the overview of the fluctuating sound analysis algorithm.

If the lower limit of the variable frequency is 10 Hz or higher, it is fixed at 200 ms. If it is below 10 Hz, the analysis frame length corresponds to the lower limit.

As mentioned in the previous chapter, fluctuation sound analysis focuses on the time variation of loudness (the perceived intensity of sound considering human hearing characteristics). Therefore, the spectral masking effect that occurs during loudness computation can also influence fluctuation sound analysis.

The example in the figure below illustrates the loudness pattern of AM (amplitude modulation) sound. The spectral masking curve extends above the carrier frequency (1 kHz), and this frequency component also varies over time. Fluctuation sound analysis analyzes the fluctuating components of both the carrier wave region and the masking region without distinction, which can result in greater fluctuations in the frequency domain affected by masking.

To eliminate this (spectral masking) effect, it is necessary to calculate fluctuation sound analysis using loudness without masking (referred to as core loudness).

* Fluctuation sound Core analysis refers to analysis using core loudness, while fluctuation sound Mask analysis includes the spectral masking effect.

Here, we explain analysis examples using the "operating sound of a car injector" and the "abnormal noise of a small motor."

Here is an example of an evaluation of the engine noise of a car.

During fuel injection, a knocking sound occurs due to the collision between the needle valve and the stopper. Although the level of this sound is not particularly loud, it is a periodic "popping" sound that is very unpleasant to hear.
The left figure shows the result of FFT analysis, where a striped pattern can be seen in the 5 kHz band. This is the source of the popping sound. The time interval of the stripes (about 40 ms) represents the period of the fluctuation.

Due to the high level of background noise in the low frequency range (below 800 Hz), it is difficult to extract this time-varying component at the level.
The right figure shows the result of fluctuating sound analysis of the same sound. The frequency axis (horizontal axis) representing the pitch of the sound is displayed densely at 5 kHz, and the fluctuating frequency axis (vertical axis) representing the period of time variation is displayed at 25 Hz. This indicates that the fluctuation of this component is significant.

The background noise component (sound below 800 Hz) that appeared prominently as noise in the FFT analysis does not respond in the fluctuating sound analysis because it is a steady sound (non-fluctuating).

Next, I will introduce an example of evaluating the operating sound of a small motor.

Due to abnormal current in the motor, a quite high-frequency "buzz" noise may occur, and the goal is to detect this as a defective product.

When comparing the OK and NG products below, the fluctuation component in the normal operating sound range (frequency: 1 kHz) can be observed in both products, but only the NG product shows significant fluctuations in the high-frequency component (8 to 10 kHz).

This component is the cause of the "buzz" noise, and to determine the pass/fail judgment of these products, it can be concluded that observing this band (frequency: 10 kHz, fluctuation frequency: 60 Hz) will allow for the judgment.