Investigation on sparse measurement on ambient noise of large-scale fan

2.1. Experimental setup

Sparse measurement applies sparse acoustic signal to sound field measurement based on spatial sparsity and optimum sparsification for locating the test-points. Firstly, the test area is gridded to form a basic test-point matrix. According to the principle of sound pressure measurement, the test area is meshed equally to form grid points, and the mathematical model for the position coordinate matrix of the grid points is established. Secondly, the location model of test-points is optimized by matrix operation of the constraint conditions of the test-points and sound field behaviors, so as to design the reasonable sparse positions. This procedure is shown in Fig. 1, where, $Y$ represents the matrix of sparse points, which is the optimized vector of test-points, and $\mathrm{\Gamma }$, $\mathrm{\Omega }$ and $\theta$ are the sparse matrix, basic matrix of test-points and degree vector, respectively. The number of non-zero components in $\theta$ is called sparsity. They are transformed as follow:

In Eq. (1), $\mathrm{\Omega }$ and $\theta$ are two critical parameters for optimizing sparse test-points.

Fig. 1Mathematical optimization procedure of sparsification

Fig. 2Sparse measurement matrix

2.2. Sparse measurement matrix and sparsity

A sparse measurement matrix is obtained by optimizing the constraints of structure and behavior in terms of the model of fundamental test-points. The procedure includes: a) establishing the matrix model of fundamental test-points; b) setting the optimum conditions of structure and behavior; c) computing the optimum matrix. This procedure transforms the layout of test-points into the simple and fast optimizing operation of test-point matrix. The sparse measurement matrix is shown in Fig. 2.

3.1. Working conditions

The sound source is located at 2 m away from the ground and 1.5 m away from the door of the fan room. The working conditions of field measurement are shown in Fig. 3.

Fig. 3Sound source position of inside and outside door

3.2. Requirements on measurement apparatus

A fan is generally a steady sound source. The microphone B&K1/2-inch40 AI, displacement sensor LANCE and data acquisition system SCADASIII305 are implemented to collect outdoor noise. The vibro-acoustic test & analytical platform LMS Test.lab is employed to process and analyze the tested data. Where, the sensitivities of the microphone and displacement sensor are set as 46.34 mv/pa and 497.6 mv/g, respectively, and the test-frequency is set as 0.2-2500 Hz.

The measurement apparatus, calibrating instruments and test-scheme are carried out strictly according to national standard GB 22337-2008, entitled “Standards of Noise Emission into Social Living Environment”. The frequency-resolutions of noise and vibration are set identical to be 1 Hz, and all frequency-spectra are computed in 10 times of average.

3.3. Layout of sparse test-points

According to the working conditions and the characteristics of fan vibration and noise propagation, the maximum SNR of single microphone is set as 8 dB resulted from the proposed scheme of sparse measurement. Additionally, by the statistics and optimization of the test-points, the layout of test-points is sparsified as shown in Fig. 4. The two-dimensional coordinates of every sparse point are listed in Table 1. The distance between each pair of test-points should not be less than 5 m, and the distance from all test-points to the wall should not be less than 1 m.

Fig. 4Layout of sparse testing points

3.4. Tested results

The vibrations and noises in different indoor and outdoor zones are tested at the sparse points, including linear and A-weighted sound pressure levels, 1/3-octave sound pressure distributions, sound pressure power and vibration spectra. The tested results are presented as follow.

(1) Tested results of indoor zone (Figs. 5-8).

Figs. 5-7 show that, the indoor sound pressure level is 84 dB and 66 dB(A) at normal running state of the fan, which illustrates that the fan noise is primarily concentrated at low frequencies, see Fig. 5; The major 1/3 octave sound pressure levels are distributed on the low frequency bands, see Fig. 6; The dominant vibrational components are at the resonant frequencies with base frequency at 215 Hz, see Fig. 8.

(2) Tested results of outdoor zones on left and right sides of corridors (Figs. 9-11).

There are most frequent activities of people on both sides of corridors. They must be the critical test zones, for which 10 points are sparsely located. The tested results at point 4 on left side of corridor and point 10 on right side of corridor are chosen here to be compared and analyzed.

Fig. 9 shows that the A-weighted sound pressure levels at points 4 and 10 are 44 dB(A) and 42 dB(A) respectively, i.e., 2 dB(A) difference between the two points. Fig. 10 shows the distribution of 1/3 octave sound pressure levels at 10 second. The low-frequency 1/3 octave sound pressure level at point 4 is slightly higher than that at point 10. The little difference demonstrates that the fan noise is primarily dominated by the frequencies below 250 Hz. Fig. 11 compares the vibration spectra between the two points, which shows that the resonant vibrations are still prominent with base frequency 215 Hz, and the vibration at point 10 is slightly smaller, but the frequency-distribution on both sides is essentially identical.

Fig. 5Sound pressure level (A-weighted-red; linear-blue)

Fig. 6The 1/3-octave sound pressure le

Fig. 7Sound pressure power spectrum

Fig. 8Vibration spectrum

Fig. 9A-weighted sound pressure level on left and right sides of the corridors

a) Point 4

b) Point 10

Fig. 101/3-octave sound pressure level distribution on left and right sides of the corridors

a) Point 4

b) Point 10

Fig. 11Ground vibration spectrum on left and right sides of the corridors

a) Point 4

b) Point 10