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SOUND QUALITY EVALUATION OF FAN NOISE BASED ON HEARING-RELATED PARAMETERS

Roland SOTTEK, Klaus GENUIT HEAD acoustics GmbH, Ebertstr. 30a 52134 Herzogenrath, GERMANY

SUMMARY Sound quality evaluation of fan noise is a challenge due to its spectral and temporal structures. Tonal components and modulated sounds are often the cause of customer complaints. Thus, besides frequency-weighted level like dB(A) or loudness, other parameters are required. In recent years, a “Hearing Model” was developed with the intention of explaining and describing psychoacoustic effects. Applying the Hearing Model to sound quality tasks allows evaluating the spectral and temporal patterns of a sound (“Relative Approach” analysis) where absolute level or loudness is often without significance. The Relative Approach analysis emphasizes all relevant signal components concerning human auditory perception: tonal and transient signals.

INTRODUCTION Many products and applications employ or include fans, for example Information Technology (IT) devices and products, household appliances, air-conditioning systems and automotive applications. Low-noise design is a key purchase requirement in all of these fields, where often the main noise source is a fan. For given constraints, such as fan dimensions and cooling performance, it is not possible by technical means to achieve an arbitrary low-noise design. The effective characterization of fan noise is a challenge in acoustic and sound quality measurement. In general, the product sound quality does not depend only on the emitted noise level or frequency-weighted level like dB(A) or loudness. Tonal components, howling sounds and modulated signals are often the cause of customer complaints. Loudness has been introduced as a more hearing-related parameter than A-weighted level in the last decades. Several methods exist in international standards for measuring the loudness of stationary signals (ISO 532 B and DIN 45631). DIN 45631 will be extended with respect to loudness of timevarying signals soon (DIN 45631/A1). This is an important step, because in practice we almost always have to deal with time-varying signals. Besides time-varying loudness, other psychoacoustic parameters like sharpness and roughness can be used for sound quality evaluation. Sharpness considers the amount of high frequency components of a noise, and roughness evaluates modulation characteristics. In addition, we developed a metric combining modulation spectral analysis with loudness calculation. In recent years, a “Hearing Model” was developed with the intention of explaining and describing psychoacoustic effects. Applying the Hearing Model to sound quality tasks allows evaluating the _______________________________________________________________________________ Fan Noise 2007

Lyon (France) 17-19 September 2007

Fan Noise 2007 Lyon (France), 17-19 September 2007

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spectral and temporal patterns of a sound (“Relative Approach” analysis) where absolute level or loudness is often without significance. The Relative Approach analysis emphasizes all relevant signal components concerning human auditory perception: tonal and transient signals. The paper starts with an overview of the Hearing Model and the Relative Approach analysis. Then a description of an extended modulation spectral analysis is given. The different methods are applied to several examples for effective sound quality evaluation of fan noise.

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THE HEARING MODEL

The basic processing steps of the Hearing Model are shown in Figure 1. The pre-processing consists of filtering with the outer ear-inner ear transfer function. Human Physiology

Hearing Model Outer and middle ear filtering (preprocess)

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The nerve cell firing rates follow the signal magnitude curve only up to a maximum frequency, modeled in a simplified manner by a 3rd-order-lowpass filter. In an additional step, the individual bandpass signals are processed using a nonlinearity as a function of the level of the exciting signal.

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Calculation of various sensations, such as specific loudness, or effects like tonal deconvolution: Other neural processing of the brain follows in the human hearing system, resulting in the different sensations such as loudness, roughness, impulsiveness, and pitch detection. Specific mathematical algorithms, such as spectral deconvolution in the case of pitch detection, are employed to describe these effects.

Figure 1: Steps of the human hearing process (top to bottom) A large number of asymmetric filters (with a high degree of overlapping) model the frequencydependent critical bandwidths and the frequency-to-place transform of the inner ear which mediates the firing of the auditory hair cells as the traveling wave from an incoming sound event progresses


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along the basilar membrane. The increasing bandwidth versus frequency of the auditory filter bank conveys a high frequency resolution at low frequencies and a high time resolution at high frequencies. The very small product of time and frequency resolution at all frequencies empowers, for example, human hearing’s recognition of short-duration low-frequency events. Subsequent rectification accounts for the fact that the nerves fire only when the basilar membrane vibrates in a specific direction. The firing rates of the nerve cells are limited to a maximum frequency. This is modeled using lowpass filters. A feature of the Hearing Model in its usual psychoacoustic application to human perception is a compressive nonlinearity relating sound pressure to perceived loudness.

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Figure 2: Functional block diagram of the Hearing Model The Hearing Model spectrum vs. time (Figure 2), however, is accessible as an intermediate result before implementing the compressive nonlinearity for modeling the relationship of sound pressure to perceived magnitude in psychoacoustic measurements (frequency scaling is shown in Bark (critical band number)), making the algorithm’s time/frequency capabilities available as a linear tool comparable to conventional techniques for events even at sound pressures beyond normal human hearing perception limits. Based on these fundamental processing steps there are a few post-processing mechanisms for calculating the basic auditory sensations. E.g., the loudness results are obtained by summing all specific loudness signals. For roughness calculation a kind of nonlinear modulation analysis and a weighting with respect to frequency and modulation rate are performed [2], [3].


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THE RELATIVE APPROACH ANALYSIS The Relative Approach method [4], [5] is an analysis tool developed to model a major characteristic of human hearing. This characteristic is the much stronger subjective response to patterns (tones and/or relatively rapid time-varying structure) than to slowly-changing levels and loudnesses. It is assumed that human hearing creates for its automatic recognition process a running reference sound (an “anchor signal”) against which it classifies tonal or temporal pattern information moment-bymoment. It evaluates the difference between the instantaneous pattern in both time and frequency and the “smooth” or less-structured content in similar time and frequency ranges. In evaluating the acoustic quality of a patterned situation, the absolute level or loudness is almost completely without significance. Temporal structures and spectral patterns are important factors in deciding whether a sound makes an annoying or disturbing impression. Subsequent to its original publication [4], the Relative Approach has been expanded in scope. Various time-dependent spectral analyses can be used as pre-processing for the Relative Approach; not only FFT-based analyses but also the Hearing Model spectrum vs. time. Hearing Model spectrum vs. time

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Figure 3: Relative Approach analysis based on the Hearing Model spectrum vs. time Recent extensions of the method give the user a choice of combining time-sensitive and frequencysensitive procedures, with adjustable priority-weighting between the two and independent settings choices for each. In this way, both time and frequency patterns in a sound situation may be


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displayed in the same measurement result (please see Figure 3). The Relative Approach algorithm objectivizes pattern(s) in accordance with perception by resolving, or extracting, them while largely rejecting pseudostationary energy. At the same time, it considers the context of the relative difference of the “patterned” and “non-patterned” magnitudes.

PSYCHOACOUSTICAL MODULATION SPECTRUM Modulation analysis is an important method for the evaluation of modulation patterns across frequency and time. The principal block diagram of the analysis is shown in Figure 4.

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Figure 4: Block diagram of modulation analysis Envelope spectra of sub-band signals are analyzed using FFT analysis. The result of such an analysis delivers information about the envelope level as a function of frequency (the center frequency of the bandpass shown in Figure 4), modulation rate (envelope fluctuations) and time. Often the degree of modulation is represented instead of the envelope level. The detectability and the evaluation of modulation patterns depend on the degree of modulation as well as on the envelope level. Therefore a psychoacoustical modulation spectrum is introduced based on two quantities: 1. envelope spectra of critical-band signals as a function of frequency (corresponding to critical band number) and modulation rate; 2. specific loudness as a function of frequency (corresponding to critical band number) according to DIN 45631/A1. The degree of modulation is calculated from the envelope spectra (Figure 5, upper left diagram) and weighted with a function w1 (N’) based on the specific loudness distribution N’(f) (Figure 5, lower left diagram). Another weighting function w2 (fm) considers the sensitivity of human hearing to modulation rate (schematically shown in Figure 5, upper right diagram). In general, this function can be dependant on the critical band number, too. The choice of the second weighting function controls the evaluation of different psychoacoustic sensations like fluctuation strength (modulation rates mainly below 10 Hz) or roughness (modulation rates mainly above 20 Hz). Figure 5, lower right diagram, shows such a psychoacoustically weighted modulation spectrum. For the calculation of a modulation metric, only values above a certain threshold will be selected.


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Figure 5: Calculation of the psychoacoustical modulation spectrum (for details please refer to text) The described method for determining a modulation metric uses standardized algorithms and is very flexible with respect to user-defined weighting functions. Thus, adaptation for different applications related to modulation analysis is easily done. Other algorithms like the Hearing Model spectrum vs. time or the Relative Approach analysis are more qualified for general sound analysis and pattern recognition respectively, but they also perform well for modulated sounds.

APPLICATION EXAMPLES In the following, four fan-noise samples of different IT devices are analyzed. The sounds were recorded using an artificial head in a hemi-anechoic chamber. Left and right channel results are averaged. The first sample (analysis results shown in the upper left diagrams of Figures 6-9) represents a quiet inconspicuous fan with a level of 24.8 dB(A) and a loudness of 0.5 sone(GF) according to DIN 45631/A1. The second and third sample (analysis results shown in the upper right and lower left diagrams of Figures 6-9) have levels of 39.0 and 40.4 dB(A), and their loudness values are 2.3 and 1.9 sone(GF). Fan noise 4 (analysis results shown in the lower right diagrams of Figures 6-9) is the loudest and most annoying fan, having a level of about 47.5 dB(A) and a loudness of 5.3 sone(GF). Fan noise 2 is judged better than fan noise 3 despite having a higher loudness. But the sharpness of fan noise 3 (1.2 acum) is the highest among all the sound samples.


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The evaluation of sound quality based on averaged psychoacoustic parameters is not very difficult if a sound is much louder and sharper than another sound, like fan noise 4 compared to fan noise 1. But in the case of similar loudness ranges the contrary effects of different signal properties have to be weighted in the right way using e.g., multiple regression analysis. Even more difficulties occur for evaluating annoying patterns: fan noise 3 contains a component at 1.35 kHz modulated with 65 Hz causing a strong roughness sensation; the roughness calculation based on the Hearing Model [2], [3] shows almost twice as much roughness compared to fan noise 2 (at present there is no standard for roughness calculation, but a DIN working group is preparing a proposal). In the case of disturbing patterns it is recommended to analyze the signal more in detail using the described algorithms. Conventional techniques such as FFT analysis often require an iterative process to determine the best combination of block size and sampling rate to display sound attributes. Often several plots are required to display all of the attributes present in a sound. Figure 6 shows as one example, a FFT vs. time analysis of the four sounds with a block size of 2048 samples (the window length is about 46 ms corresponding to a frequency resolution of 21 Hz). Fan noise 1

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Figure 6: FFT vs. time analysis using a block size of 2048 samples at a sampling rate of 44.1 kHz Since the Hearing Model always analyzes with a time and frequency resolution similar to human hearing, only one analysis of the data needs to be performed to display the complete time and frequency structure being heard by the listener. The Hearing Model makes an excellent first step in visualizing the complete hearing event. By studying the output of the Hearing Model and using interactive listening, engineers are easily guided to the best method for isolating critical attributes of a product’s sound. Figure 7 shows the Hearing Model spectra vs. time of the same sounds. The very small product of time and frequency resolution at all frequencies indicates, besides the distribution of energy over frequency, the very important time structure of the fan noise samples. The modulated components are clearly visible.


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Figure 9: Psychoacoustical modulation spectrum Finally, Figure 9 visualizes the psychoacoustical modulation spectrum. Fan noise 4 shows the most dominant modulation pattern at modulation rates of about 50 Hz and 100 Hz. This noise is perceived as the most annoying because it has the highest level, and the modulation spectrum has high values in many frequency bands for a given modulation rate (50 Hz and multiples): a characteristic for a broadband modulation. The maximum of the psychoacoustical modulation spectrum for all four sounds can be found for fan noise 3 as mentioned above.

CONCLUSIONS AND OUTLOOK One of the greatest challenges facing NVH engineers is determining the analysis method which will best display critical attributes being heard in a product’s sound. This is essential for comparing products or monitoring performance of a product during development with respect to the design objectives. The Hearing Model was born out of a widespread interest to have one standardized psychoacoustic model. There are currently several models available, such as Zwicker Loudness, which address a single psychoacoustic phenomenon. The Hearing Model describes and explains many phenomena at once. The Hearing Model is based on the physiology of human hearing and has been validated by testing against previously conducted psychoacoustic research results. The Relative Approach analysis emphasizes all relevant signal components concerning human auditory perception: tonal and transient signals. For extracting individual patterns other signalprocessing steps are necessary.


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The psychoacoustical modulation spectrum presented here has been proven a powerful tool for the analysis of modulated components, providing, besides the psychoacoustical evaluation, additional information about the physical signal properties. Heretofore, the focus was mainly on an adequate modulation spectrum as a function of frequency and modulation rate. The first results concerning the development of a modulation metric are very promising. Multiple weighting functions for frequency and modulation rate were investigated by Jeff DeMoss and Randy Stanley in a study project. A large number of fan noises were analyzed, and the results were correlated to the judgments of a group with more than 20 jurors. In the future the performance of the metric will be tested with other modulation sounds.

BIBLIOGRAPHY [1] [2] [3] [4] [5]

R. Sottek - Modelle zur Signalverarbeitung im menschlichen Gehör. Dissertation, RWTH Aachen, Germany, 1993. R. Sottek -Gehörgerechte Rauhigkeitsberechnung. DAGA ’94, Dresden, 1994. R. Sottek, P. Vranken, H.-J. Kaiser - Anwendung der gehörgerechten Rauhigkeitsberechnung. DAGA ’94, Dresden, 1994. K. Genuit - Objective evaluation of acoustic quality based on a relative approach. Internoise ’96, Liverpool, 1996. W.R. Bray - Using the “Relative Approach” for Direct Measurement of Patterns in Noise Situations, Sound and Vibration, September 2004.