Tracing the source of unsteady-state low-frequency noise based on wavelet coherence analysis

Abstract

The original partial coherence analysis method can be used to analyze the contributions between different noise sources and field points under steady-state conditions. Nevertheless, coherence analysis cannot be used to deal with unsteady-state signals because the signals are time-varying. In this paper, the method of panel contribution under unsteady-state conditions based on wavelet coherence analysis is proposed to determine the largest noise contribution in the cab. First, the unsteady-state simulation signals are analyzed by wavelet coherence theory. This step not only verifies the effectiveness but also points out that wavelet coherence is more superior to crossed wavelet. Second, the measured unsteady-state signals of the eight measuring points are processed by time-frequency wavelet coherent analysis. According to the obtained two-dimensional time-frequency diagrams, the contribution of different panels to the noise of measuring field points in the continuous frequency range can be found out. Then, the total contribution coefficient sum of each panel in a certain frequency band is calculated. Finally, the above analysis results are used to determine the panels with the largest contribution to the cab noise. The corresponding noise reduction scheme is also proposed. The results show that the overall sound pressure level is obviously decreased after optimization. The noise in the cab is reduced by 4.5dBA ∼ 7dBA. The effectiveness of this method has been further verified by the above results.

Keywords

Unsteady-state signal partial coherence analysis wavelet coherence analysis low-frequency noise panel contribution

1. Introduction

For the rapid development of the automotive industry and increased market maturity, consumers pay more attention to ride comfort. The noise in the vehicle is one of the main factors affecting driving comfort (Pang et al., 2006). Low-frequency noises in the vehicle come from the vibration of the panel caused by various excitation sources (Brown, 1998). Therefore, it is necessary to find main noise contribution of sheet metal.

Partial coherence analysis is an effective method used to analyze the correlation of steady-state noise. This method can remove the mutual influence between the coupled panels. It can also identify and locate the noise source. Furthermore, it sorted and analyzed the contributions of different noise sources and different field points (Bendat, 1976; Trethewey and Koss, 2004; Wu et al., 2008, 2012; Zhao and Wang, 2005). However, most of the signals collected in engineering tests are unsteady-state signals. Their characteristics change with time. Therefore, the original partial coherent analysis method is not applicable to the unsteady-state signals signals’ analysis. The unsteady-state signal can be processed by wavelet transform. But it cannot explore the relevant relationship between two signals (Mallat, 1998). Therefore, some researchers had proposed a wavelet coherence method to analyze the correlation of unsteady-state signals. This method was first applied to meteorological, hydrology (Torrence and Webster, 1999; Zhang et al., 2016), and EEG research (Banerjee and Mitra, 2014; Rowley et al., 2007). With the continuous development of wavelet coherence algorithms, it had gradually been applied to engineering research. The magnitude and phase relationship of the coherence function between different unsteady-state noise signals were obtained (Jia et al., 2008) from the time and frequency domain. But it failed to further explain the phase relationship between the two signals. Some scholars (Wang et al., 2015) had simulated two unsteady-state signals based on coherent wavelet transform. The effectiveness in solving the phase difference between signals was verified. Some researchers (Huang et al., 2018) used this method to identify the noise source of the car in unsteady-state driving process. The noise inside the car was effectively improved by optimizing the suspension components. However, the detailed partial coherence coefficient and phase diagram had not been obtained either. The above-mentioned research on the unsteady-state signal was to solve the problem of noise in the car from the perspective of the noise source. But these studies rarely focused on the perspective of sheet metal contribution. As the cab was a closed space, the vibration of the cab panel will directly affect the noise in the cab (Mohanty et al., 2000). In addition, the vibration of the panel at different positions had different effects on the noise inside the car, which were the contribution of the panel (Liu et al., 2011; Yang et al., 2016). Therefore, wavelet coherence was introduced into the analysis of panel contribution. Then, the phase relationship between different unsteady-state signals and the contribution of different panels to noise can be solved.

Aiming at the noise proble in the cab of a certain heavy truck, this paper proposes the methods of panel contribution based on wavelet coherence analysis to research the contribution of the cab panel. First, the unsteady-state signals collected by one heavy truck are processed by wavelet coherence analysis. Second, the wavelet time-frequency coherence diagrams between two unsteady-state signals is obtained. From this foundation, the unsteady-state signals are analyzed. The relevant relationship between the panel vibration signals and the noise signals in the cab in the continuous frequency range is found. Furthermore, the concept of “total contribution coefficient sum” is introduced in this paper. It can calculate the total contribution coefficient sum of each panel to the whole system in a certain frequency band. Finally, the above analysis results are integrated to find the panels which have the largest contribution. Also, a reasonable noise reduction scheme is proposed. The results not only verify that is suitable for the correlation analysis of unsteady-state noise signals but also effectively improve the acoustic environment of the heavy-duty truck cab. It provides a certain reference for solving the problem of unsteady-state signals’ coherent analysis in engineering applications.

2. Wavelet coherence analysis theory

In this paper, when processing the unsteady signals the appropriate wavelet basis function should be selected first. In engineering applications, the amplitude wavelet Morlet wavelet is regularly selected to obtain the amplitude and phase information. The Morlet wavelet function is defined in the time and frequency domain as

ψ_{0} (η) = π^{- 1 / 4} e^{i ω_{0} t} e^{- t^{2} / 2}

(1)

The center frequency $ω_{0}$ of the wavelet function is generally taken as six to meet the requirements of admissibility conditions. At this time, simultaneous positioning in both time and frequency domain can be provided by this wavelet function (Torrence and Webster, 1999).

For the signal $x (t)$ , when Morlet is used for calculation, its continuous wavelet transform is

W_{n}^{X} (s) = \sqrt{\frac{δ_{t}}{s}} \sum_{n^{'} = 1}^{N} x_{n^{'}} ψ_{0} [(n^{'} - n) \frac{δ_{t}}{s}]

(2)

where

ψ_{0}

represents the wavelet basis function of formula (1).

δ_{t}

and

N

are the sampling interval and the number of points of the signal

x (t)

, respectively.

s

represents the transform scale of continuous wavelet transform

W_{n}^{X} (s)

. Through different combinations of scale

s

and time

t

, the time-frequency distribution of the signal can be calculated (Zhou, 2010).

The two unsteady-state signals are processed by wavelet coherence analysis to study the relevant relationship in the time-frequency domain. This method can be used to calculate the correlation magnitude and phase relationship between two signals. The wavelet coherence analysis method is formed by combining wavelet transform and coherent analysis. It mainly includes two methods: cross wavelet transform and wavelet coherence. How to use these two methods for coherent analysis of unsteady signals will be discussed next.

2.1. Cross wavelet transform

Wavelet transform can be used to explore the inherent laws of unsteady-state signals. But it cannot distinguish the correlation between two unsteady-state signals in the time-frequency domain. The cross wavelet transform not only combines with the advantages of the wavelet transform but also targets the common high-energy region existing between two unsteady-state signals. Therefore, the amplitude and phase relationship between the two signals can be solved simultaneously in the time and frequency domain. The effect is remarkable.

According to formula (2), let $W_{n}^{X} (l)$ and $W_{n}^{Y} (l)$ be the continuous wavelet transform of the unsteady-state signals $x (t)$ and $y (t)$ . The cross wavelet power spectra of $x (t)$ and $y (t)$ is defined as

W_{n}^{X Y} = W_{n}^{X} (l) \times [W_{n}^{Y} {(l)}^{*}]

(3)

where

W_{n}^{X} (l)

is the continuous wavelet transform of

x (t)

W_{n}^{Y} {(l)}^{*}

is the complex conjugate of

y (t)

after wavelet transform.

W_{n}^{X Y}

is represented by the cross wavelet power spectrum between

x (t)

and

y (t)

. The value of

W_{n}^{X Y}

is larger, and the correlation between the two signals is greater. The number tangent of

W_{n}^{X Y}

represents the phase relationship between the two signals.

Cross wavelet transform is formed by combining the wavelet transform of formula (2) and cross spectrum analysis. Therefore, it is necessary to perform a certain level of significance test to ensure that the calculation results are accurate and reliable of the cross wavelet power spectrum. This is generally tested by comparing the cross wavelet power spectrum of the two signals with the red noise spectrum. The function of red noise is

P_{k} = \frac{1 - α^{2}}{{| 1 - α e^{- 2 i π k} |}^{2}}

(4)

where

k

is the frequency index and

α

is the correlation coefficient in the autoregressive equation (Zhang et al., 2007).

2.2. Wavelet coherence analysis

The research object of this paper is the cab of a heavy truck. However, in the actual driving process of the vehicle, most of the collected signals are unsteady-state signals. When two unsteady-state signals have a common high-energy part, the cross wavelet analysis method in the section 2.1 is frequently used to analyze the correlation between two signals. The effect of analysis is remarkable. But there are shortcomings in revealing the correlation between the two unsteady-state signals in the common low-energy region. Nevertheless, the wavelet coherent method can make up for the shortcomings of crossed wavelets. When processing the high common energy region of two unsteady-state signals, it can also consider low common energy regions. It can obtain the amplitude relationship and phase relationship of two unsteady-state signals in the time-frequency domain. Therefore, wavelet coherence can be used to describe the local correlation between two unsteady-state signals. According to formula (3), the wavelet coherent spectra of two unsteady-state signals $x (t)$ and $y (t)$ is defined as

R_{n}^{2} (l) = \frac{{| S [l^{- 1} W_{n}^{X Y} (l)] |}^{2}}{S [l^{- 1} {| W_{n}^{X} (l) |}^{2}] \cdot S [l^{- 1} {| W_{n}^{Y} (l) |}^{2}]}

(5)

where

R_{n}^{2} (l)

represents the correlation between two unsteady-state signals.

S

is the smoother. Its expression is

S (W_{n}) = S_{S} {S_{t} [W_{n} (l)]}

where

S_{t}

represents smoothing on the time axis.

S_{S}

represents smoothing on the scale axis.

The basis of wavelet coherence analysis is the wavelet transform of formula (2). Therefore, it must be tested under a certain level of confidence after calculating the wavelet coherence spectrum. The commonly used test method is the Monte Carlo method (Zhang et al., 2007).

3. Total contribution coefficient sum

After the road test of the heavy truck, a suitable model is needed to calculate the collected data. When using the multiple-input single-output model for calculation, multiple-input signals should be sorted according to the certain rules (Hu et al., 2012). After replacing the original input signals with the sorted input signals, the multiple-input single-output system becomes a multiple-input single-output system. The specific process is shown in Figure 1.

Figure 1.

Multiple-input single-output model.

The capital letter $X$ represents the Fourier transform of each signal. “!” means that each vibration signal removes the relative influence between each other. In this case, the input signals or the output signals in the system are independent of each other. $X_{i \cdot (i - 1)!}$ represents that the relevant influence of the original signal $X_{1}$ , $X_{2}$ , ..., $X_{i - 1}$ on X_i have been removed. $q$ represents the number of input signals. $L_{1 y}$ , $L_{2 y}$ , ..., $L_{q y}$ represent the optimal frequency response function (FRF) of the system. The input subscript is placed before the output subscript. $N$ represents the interference of environmental noise. $Y$ represents the output signals.

Aiming at how to measure the impact of each input overall, this paper introduces the concept of “total contribution coefficient sum.” Total contribution coefficient sum is the characterization of the sheet metal contribution. It is defined as the sum of the wavelet coherence coefficient values of a certain input signal $X_{i}$ to the output signals $Y$ in a certain frequency range, and the function is expressed as

P_{F}^{s u m} = \sum_{j = 1}^{n} P_{j}

(6)

where

P_{F}^{s u m}

represents the total contribution coefficient sum of the input signals

X_{i}

to the entire system in a certain frequency range. This system is the multiple-input single-output system shown in Figure 1.

P_{j}

represents the wavelet coherence coefficient value of the input signals

X_{i}

to the output signals

Y

n

is the number of input signals of the same type (Song, 2006).

4. Wavelet coherence analysis of unsteady-state signal

4.1. Unsteady-state simulation signal

In this section, the non-orthogonal Morlet wavelet function of formula (1) is selected as the basis function when using the wavelet coherent analysis method to process the unsteady-state simulation signals. A set of non-stationary analog signals are designed to verify the effectiveness of wavelet coherence method. The input signals and output signal are as follows:

Input signal 1: $x_{1} (t) = 0.8 \cos (2 π f_{1} t_{1}) + 0.3 \cos (2 π f_{2} t_{2}) + 0.1 r a n d n [1, l e n g t h (t_{1})]$

Input signal 2: $x_{2} (t) = 0.2 \cos (2 π f_{2} t_{1}) + 0.9 \cos (2 π f_{3} t_{2}) + 0.2 r a n d n [1, l e n g t h (t_{2})]$

Output signal 3:

x_{3} (t) = 0.6 \cos (2 π f_{1} t_{3} - \frac{π}{4}) + 0.4 \cos (2 π f_{2} t_{4} + \frac{π}{2}) + 0.8 \cos (2 π f_{3} t_{5}) + 0.3 r a n d n [1, l e n g t h (t_{5})]

where

f_{1} = 16 H z

f_{2} = 64 H z

f_{3} = 128 H z

t_{1} \in [0,1] s

t_{2} \in [1,2] s

t_{3} \in [0,0.5] s

t_{4} \in [0.5, 1.5] s

, and

t_{5} \in [1.5, 2] s

r a n d n [1, l e n g t h (t)]

is used to generate the Gaussian white noise signal. It can be used to generate random numbers whose elements

1

and

l e n g t h (t)

obey the standard normal distribution where

l e n g t h (t)

represents the length of time

t

First, the method of cross wavelet transform is used to process the simulation signal. The correlation between the two unsteady-state signals can be obtained. Second, the two input signals $x_{1} (t)$ , $x_{2} (t)$ , and the output signal $x_{3} (t)$ are processed, respectively, by cross wavelet using formula (3). The cross wavelet transform diagrams are shown in Figure 2. Then, it is processed by wavelet coherence using formula (5). Finally, the coherence coefficient diagram and phase diagram between the two signals are obtained. Figure 3 and Figure 4 show the wavelet coherence distribution diagrams.

Figure 2.

Cross wavelet transform diagrams: (a) cross wavelet diagram of $x_{1} (t)$ and $x_{3} (t)$ and (b) Cross wavelet diagram of $x_{2} (t)$ and $x_{3} (t)$ .

Figure 3.

Wavelet coherence diagram of $x_{1} (t)$ and $x_{3} (t)$ : (a) correlation coefficient diagram and (b) phase diagram.

Figure 4.

Wavelet coherence diagram of $x_{2} (t)$ and $x_{3} (t)$ : (a) correlation coefficient diagram and (b) phase diagram.

In Figure 2, the reciprocal of the period multiplied by the sampling frequency is the actual frequency of the signal. The sampling frequency here is $1024 H z$ . Equation (4) is used to test the significance of the calculated results of the crossed wavelet power spectrum. Then, the cross wavelet power spectrum of the two signals is compared with the red noise spectrum. The enclosed area by the black curve in Figure 2 indicates that the calculation result has passed the 95% confidence test.

Figure 3(a) and Figure 4(a) are three-dimensional diagrams of coherence coefficient between the two input signals ( $x_{1} (t)$ , $x_{2} (t)$ ) and the output signal $x_{3} (t)$ , respectively. These figures simultaneously show the correlation between them in the time and the frequency domain. Two highlighted areas can be clearly seen in these figures. The coherence values in these areas are both greater than 0.8. Figure 3(b) and Figure 4(b) are phase diagrams between the two input signals ( $x_{1} (t)$ , $x_{2} (t)$ ) and the output signal $x_{3} (t)$ , respectively. The bright color of the area in the figure indicates that the phase angle is a positive value. The brighter the color, the larger the value. On the contrary, the dark color of the area indicates that the phase angle is a negative value. The darker the color, the smaller the value.

In practical engineering applications, the coherence coefficient diagram and the phase diagram are combined to facilitate judgment. The wavelet coherent time-frequency diagrams between $x_{1} (t)$ and $x_{3} (t)$ , $x_{2} (t)$ and $x_{3} (t)$ are shown in Figure 5.

Figure 5.

Wavelet coherence diagram of simulated signal: (a) wavelet coherent time-frequency diagram of $x_{1} (t)$ and $x_{3} (t)$ and (b) wavelet coherent time-frequency diagram of $x_{2} (t)$ and $x_{3} (t)$ .

The lightness and darkness of the colors in the figure indicate the degree of correlation between the input and output signals. The color is brighter, and the correlation between the two signals is stronger (Huang et al., 2018). The arrow indicates the phase relationship between the two signals. The counterclockwise angle between the arrow and the horizontal line of the positive half axis indicates the phase value of the output signal lagging behind the input signal.

According to Figure 5, the input signals $x_{1} (t)$ and $x_{2} (t)$ have a strong correlation with the output signal $x_{3} (t)$ in different time periods and in the central area of $16 H z$ or $64 H z$ . The calculated results are consistent with the physical characteristics of unsteady-state simulation signals. The above analysis results verify the effectiveness of wavelet coherence analysis in unsteady-state signal processing.

4.2. Coherent analysis of vehicle acceleration signal

Taking the cab of one heavy truck as the research object, it is necessary to carry out a road test on the vehicle. The test is in accordance with the relevant operating specifications stipulated in the GB/T 18697-2002 “acoustics-measurement of noise inside motor vehicles.” The cab panel vibration and noise are collected.

The measuring points of the panel are preliminarily divided. Here, the body panels of the cab are divided into six parts. Points are distributed evenly on each board to avoid missing important signals during testing. Then, acceleration sensors are placed at each measuring point to collect vibration signals. The preliminarily divided measuring points of the panel are shown in Table 1.

Table 1.

Measuring points of the panel after preliminary division.

Panel number	Position	Number of measuring points
1	Right side panel	24
2	Right door	11
3	Left side panel	30
4	Left door	11
5	Rear panel	23

When the vehicle is stationary, we knock each panel by a force hammer to cause vibrations in sequence. Each measuring point is knocked three times to avoid accidental operation. The FRF of the panel is obtained in real time. The main energy boundary of signals in the cab is in low-frequency range. Therefore, the points where the FRF has obvious peaks in the frequency range of

30 - 60 H z

and

80 - 120 H z

are selected as the final panel measuring points. These final selected panels are divided and numbered in details. The positions of the measuring points are given in Table 2. Figure 6 displays a certain heavy-duty truck marked with key measuring panels. As shown in Figure 7, stickable labels are used to mark these positions to avoid missing any points and only positions of key panels are shown.

Table 2.

Position of measuring points after the final division.

Measuring points	Position	Measuring points	Position	Measuring points	Position
1	Right side panel 3	11	Left door 10	21	Right door 4
2	Right side panel 6	12	Left door 6	22	Left panel 30
3	Right side panel 11	13	Rear panel 12	23	Left panel 11
4	Right door 3	14	Rear panel 1	24	Left panel 20
5	Right door 10	15	Rear panel 2	25	Left panel 5
6	Right door 7	16	Rear panel 3	26	Left door 11
7	Right door 11	17	Right side panel 9	27	Left door 9
8	Left side panel 22	18	Right side panel 5	28	Left door 7
9	Left side panel 14	19	Right side panel 24	29	Rear panel 20
10	Left side panel 24	20	Right side panel 8	30	Rear panel 13

Figure 6.

Test vehicle. 1. Left door; 2. left side panel; 3. left panel; 4. rear panel.

Figure 7.

Location figure of measuring points for key panels: (a) right side panel and (b) rear panel.

Three-way acceleration sensors are arranged at the corresponding measuring points. They are adsorbed on the sheet metal parts of the cab using magnetic bases. Then the data is collected by the Siemens-LMS system. The equipment used in the test are listed in Table 3. Figure 8 displays the LMS data acquisition and the analysis system placed in the heavy truck. Figure 9 displays the installation diagram of the sound level meter on the main driver’s right ear.

Table 3.

Test equipment.

	Equipment name	Model and main technical indicators	Function specification
Hardware	Siemens-LMS data acquisition system	Model: SCM2E05, SCM-V8-E and SCM-MS	Real-time acquisition of noise signals to the computer
	Three-axis acceleration sensor	Model: 356A16, Sensitivity: 100 mV/g	Measure the acceleration of the panel in the X, Y and Z directions
	Force hammer	Model: 086C03, Sensitivity: 4pC/N	Knock the panel to make the panel vibrate
	Sound level meter	Model: 378B02, Actual sensitivity: 67.907mv/Pa	Convert noise signals into electrical signals
	Sound level meter calibrator	Model: CAL200	Calibrate the sound level meter
Software	Siemens-LMS Testlab software	TX-DPR.99.1 and TX-TDA.10.2	Recording, analysis and processing of noise signals in real time

Figure 8.

LMS data acquisition and analysis system: LMS data acquisition system and 2. LMS software.

Figure 9.

Installation diagram of the sound level meter: (a) location figure of sound level meter and (b) main driver’s right ear measurement point.

The test condition is that the speed of the heavy truck is accelerated evenly from 60 km/h to 70 km/h. The sampling frequency is $6400 H z$ . The test road is a straight asphalt pavement with no noise interference around. The LMS. testlab software is used for real-time data acquisition and synchronous recording during the road test. At this time, the cab panel is in unsteady-state vibration. Therefore, the vibration signals of all panels’ measuring points and the sound pressure signals at the position of the driver’s right ear are collected simultaneously. The test was repeated three times to ensure the accuracy.

According to the recorded data of the LMS software, the data of each measuring point in the period of $1.35 s - 9.35 s$ (corresponding to the speed of $60 - 70 k m$ ) are selected. The multiple-input single-output model shown in Figure 1 is used for analysis. Then, the vibration and sound pressure signal at the position of each measuring point is processed by wavelet coherence. Here, the sound pressure signal at the position of the right ear of the main driver is selected as a representative for coherent processing. Equation (6) is used to solve the total contribution coefficient sum of each measuring point in the frequency range of $30 - 60 H z$ and $80 - 120 H z$ . Since there are too many measuring points, two representative measuring points with larger correlation coefficients are selected in each cab panel for comparison. Figure 10 shows the representative wavelet coherence diagrams of these measuring points obtained after processing.

Figure 10.

Wavelet coherence diagram between panel vibration and noise signal of the main driver’s right ear: (a) measuring point 6; (b) measuring point 9; (c) measuring point 12; (d) measuring point 15; (e) measuring point 18; (f) measuring point 19; (g) measuring point 23; and (h) measuring point 29.

It can be seen from Figure 10 that when the frequency is below $16 H z$ , the vibrations of all measuring points have obvious related relationship with the sound pressure of measuring points in the period of $4 - 8 s$ . When the frequency is in the area centered at $64 H z$ , the noise signals of measuring point 9 has a strong correlation with that of main driver’s right ear in the period of $0 - 4 s$ . The noise signals of measuring point 23 has a strong correlation with that of main driver’s right ear in the period of $4 - 8 s$ . The phase difference between the noise signal of two measuring points is $π / 4$ . The correlation values of the above two measuring points exceed 0.8. When the frequency is in the $2 - 16 H z$ region, measuring point 15 has obvious relationship with that in the entire period of $0 - 8 s$ . The above noise signals of three measurement points have the largest coherence coefficient values.

To sum up, when the left side wall of the cab is subject to low-frequency excitation, it has the largest contribution to the driver’s right ear. The rear panel has great influence on the interior noise in the whole low frequency band. Therefore, it is determined that the panels that have the largest noise contribution to the cab are the rear panel and the left side panel area.

Based on the above test results, the positions of the panel have been determined. The noise in the cab can be suppressed when sound absorption measures are taken on the corresponding panel.

5. Optimization verification of damping treatment

Through previous analysis, the panels that contribute significant noise in the cab are determined. These panels with excessive vibration must be optimized to reduce the noise in the cab. There are two commonly used noise reduction methods: active noise reduction and passive noise reduction. The manufacturing cost of active noise reduction is relatively high. Its algorithm is too complex to adapt to the improvement of mass-produced vehicles. Therefore, it cannot be used in heavy truck cab described here. The commonly used passive noise reduction methods include structural optimization and damping treatment (Li, 2005). In practical engineering applications, the optimal solution of structural optimization should be adjusted according to specific working conditions. The damping treatment can absorb vibration energy without affecting the overall dynamic and static characteristics of the car body, which makes the optimization simple. Therefore, sticking aluminum foil butyl rubber damping materials on the rear panel and left side area of the cab panel is adopted to reduce the low-frequency noise in the vehicle. The pasting positions of the material are shown in Figure 11.

Figure 11.

Damping paste diagram: (a) paste diagram of rear panel damping and (b) paste diagram of left side damping.

A road test is carried out with above optimization means to verify the feasibility of the method. The LMS equipment is used to collect and analyze the sound pressure signal at the position of driver’s right ear. By comparing the results before and after optimization of the sound pressure of the measuring point, we can see the noise reduction effect after damping treatment. The sound pressure signal is processed by spectrum analysis. The frequency spectrum of the sound pressure signals before and after the improvement is shown in Figure 12. Figure 13 displays the comparison results of the one-third octave power spectrum and overall sound pressure level before and after the improvement.

Figure 12.

Spectrum diagram of sound pressure level before and after optimization.

Figure 13.

Comparison diagram of one-third octave power spectrum and overall sound pressure level before and after improvement. “MD” represents the right ear of the main driver. “CO” represents the right ear of the co-pilot. (a) One-third octave power spectrum, (b) overall sound pressure level.

From Figure 12, in the main driving position, the sound pressure at the right ear drops by about $7 d B A$ , 5dBA and 1dBA respectively in the $55.2 H z$ , 110.0Hz and 201.5Hz frequency band. From Figure 13(a), at 110.0 Hz and 201.5 Hz one-third octave band, the sound pressure is smaller than before optimization. But at 55.2 Hz, one-third octave band, the sound pressure is slightly larger than before optimization. Therefore, although the sound pressure near few peaks in Figure 12 is increased, the cumulative power spectrum of the corresponding frequency bands of these peaks is mostly reduced. Furthermore, when the optimized vehicle is driven at 70 km/h with a full load, the overall sound pressure level of the main driver’s right ear drops from 59.04 dBA to 54.59 dBA. This value has dropped by about 4.5 dBA. The above results show not only that the noise reduction effect is remarkable but also the sound environment in the cab of the heavy truck is effectively improved.

6. Conclusion

In this paper, the method of panel contribution based on wavelet coherence analysis is proposed to analyze the contribution of cab panels. The correlation magnitude and phase relationship between the two unsteady-state signals are obtained. The contribution of different panels to the noise of the measuring point can be found by this method in continuous frequency range. It also solves the problem that traditional methods are not suitable for solving continuous peaks on the time varying state. The effect is significant dealing with multiple peaks of low-frequency noise in the car. By combining with the contribution of sheet metals, the panels that had the largest contribution to the cab noise in the main frequency range are found. The road test shows that the noise level in the cab can be effectively reduced by pasting the damping material on the panels with the largest noise contribution. The effectiveness of this method is verified, and a reasonable noise reduction method in engineering applications is put forward. This paper provide a valuable reference for relationship analysis between different unsteady-state signals.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Yongzhen Chen

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