A generalized inverse cascade method to identify and optimize vehicle interior noise sources

Journal Pre-proof A generalized inverse cascade method to identify and optimize vehicle interior noise sources H.B. Huang, J.H. Wu, X.R. Huang, M.L. Yang, W.P. Ding PII:

S0022-460X(19)30625-X

DOI:

https://doi.org/10.1016/j.jsv.2019.115062

Reference:

YJSVI 115062

To appear in:

Journal of Sound and Vibration

Received Date: 25 March 2019 Revised Date:

8 October 2019

Accepted Date: 30 October 2019

Please cite this article as: H.B. Huang, J.H. Wu, X.R. Huang, M.L. Yang, W.P. Ding, A generalized inverse cascade method to identify and optimize vehicle interior noise sources, Journal of Sound and Vibration (2019), doi: https://doi.org/10.1016/j.jsv.2019.115062. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.

A Generalized Inverse Cascade Method to Identify and Optimize Vehicle Interior Noise Sources

H. B. Huang a, b, J. H. Wu a, X. R. Huang c, d, M. L. Yang b, W. P. Ding b, *

a

School of Mechanical Engineering, Xi’an Jiaotong University, 710049 Xi An, Shaanxi, China

b

Engineering Research Center of Advanced Driving Energy-saving Technology, Ministry of Education,

610031, Cheng Du, Si Chuan, China c

School of Automobile and Transportation, Xihua University, Chengdu, 610039, China

d

Department of Electrical Engineering & Computer Science, College of Engineering and Applied

Science, University of Cincinnati, Cincinnati, Ohio, 45221-0030, USA

*Corresponding author: W. P. Ding Tel.: +86(028)87600695 E-mail: [email protected]

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Abstract: The noise, vibration and harshness (NVH) emitted by a vehicle are very important to a customer’s perception of the vehicle quality. A vehicle’s NVH can be improved by considering the three following facets: the noise source, transfer path, and receiver. The identification and optimization of vehicle interior noise sources is crucial when attempting to reduce noise levels and improve sound quality. Although traditional methods, such as those utilizing sound pressure levels, nearfield acoustic holography, and transfer path analysis, can provide the magnitudes and contributions of noise sources, they cannot present specific methods for optimizing those noise sources. This study proposes a new method, the generalized inverse cascade method (GICM), to solve this problem. The GICM combines systems engineering with the interval optimization technique to identify and optimize vehicle noise sources. Applying the GICM to a decision problem involves the following three steps: (1) constructing the decision problem as a cascade tree; (2) developing a numerical model to quantify the cascade tree; and (3) solving the numerical model using the interval optimization method. A Volkswagen sedan is used in this study as an example, and a vehicular road test and subjective evaluation are implemented to record and evaluate the interior noise. The GICM, identifies potential abnormal interior noise sources, and a modified method is presented to optimize the abnormal noise sources by calculating the feasible intervals of design variables. A verification experiment shows that the vehicle interior noise is successfully optimized, thereby validating the proposed GICM.

Keywords: Interior noise; Cascade tree; Noise source identification; Noise source optimization; Feasible intervals

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1. Introduction The noise, vibration and harshness (NVH), a multidimensional attribute dependent on time and frequency interactions, emitted by a vehicle plays an important role for consumers in the purchase of a vehicle. Consequently, many researchers and engineers have focused on studying the NVH to improve vehicle quality. Over many years of research, the principal sources of engine noise have been identified and significantly reduced. Hence, vehicles have become increasingly quiet, especially new, purely electric vehicles, which have no internal combustion engine [1]. As a consequence, the vehicle interior noise threshold, which constitutes the new noise floor, is being approached; however, reaching this threshold will limit the benefits gained by further reducing these dominant components unless the noise sources that result in this threshold are reduced [2,3]. Accordingly, further improving the NVH is a challenging task in vehicle design and troubleshooting (D&T). The vehicle NVH can be improved by considering three facets: the noise source, transfer path, and receiver. The identification of vehicle interior noise sources is fundamental for reducing noise levels and improving sound quality. Unfortunately, due to the variability and richness of vehicle interior noise, it is almost impossible to recognize complicated noise sources directly. Therefore, a common noise source identification system often consists of four key steps: data acquisition, signal processing, noise source identification and noise source optimization. Many factors influence vehicle interior noise. The potential sources of interior noise can be divided into two categories in terms of the transfer path [4,5]: airborne noise sources and structure-borne noise sources. Tire/road noise, engine/motor noise and wind noise are airborne noise sources. Airborne noise can be collected through a microphone. Moreover, most airborne noise is emitted at a high frequency and thus could be reduced via the use of sound insulation and absorption materials within the vehicle [6].

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Structure-borne noise sources, including suspension vibration noise, engine vibration noise, and subframe vibration noise, are generated from the vibrations of the vehicle structure. Structure-borne noise is relatively complex, and its analysis can be confusing [7,8]; therefore, a specific reference signal (such as the acceleration, velocity, or force) that is coherent with the noise source is commonly used to evaluate radiation noise indirectly. Structure-borne noises are emitted mainly at low and medium frequencies, i.e., less than 1 kHz, and could be reduced by controlling structural vibrations [9]. In recent years, many researchers have reported great contributions to the identification of vehicle interior noise sources [10-20]. The finite element method (FEM), the sound intensity technique, time-frequency analysis, nearfield acoustic holography (NAH), and transfer path analysis (TPA) are widely used to identify interior noise sources. In [10], the FEM is used to predict the sound pressure level (SPL) in a vehicle cabin, and the contribution of each radiating panel to the interior noise level is determined. In [11], sound intensity techniques are applied to analyze the interior noise distribution within a vehicle, and a potential floor vibration noise source is identified. In practice, extracting signal characteristics through time-frequency analysis with sufficient precision is important for accurately identifying sources of noise. Appropriately, to evaluate vehicle interior noise, the wavelet package transform is applied in [12] to extract sound features in different frequency bands. In [13], the Wigner– Ville distribution is used to evaluate the interior sound quality, and a rattling noise source generated by suspension shock absorbers is recognized. To analyze the correlation of noise sources, a coherence-based noise source identification technique is developed to identify the contributions of combustion noise to near- and far-field acoustic measurements of aero-engines [14]. In addition, several techniques based on microphone array measurements have been developed to visualize and identify the location of noise sources intuitively [14-15]. In [15], NAH is utilized to identify the sources of

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noise emanating from an automotive muffler surface excited by a single explosion pulse to simulate a single pulse in the exhaust system. Alternatively, a method derived from NAH, the beamforming technique, has been developed to locate the sources of noise during the passage of a car and to obtain additional insight into the noise characteristics [16]. TPA is another advanced technique for recognizing noise and vibration sources within a system and is widely used in the mechanical industry [17]. In [18], TPA is used to evaluate the structure-borne noise originating from the bogie of a high-speed railway vehicle and to determine the contribution ratio according to the transfer path. Furthermore, operational TPA has been proposed to identify the dominant sound path in a vehicle to reduce interior noise [19]. Other TPA-derived methods, such as fast TPA and hybrid TPA, have also been developed for specific applications [20]. Based on the above analysis, many noise source identification methods have been successfully applied to address the airborne and structure-borne noise problems in vehicle interiors. However, previous studies [10-20] suffered from some common characteristics and problems as follows: SPL and sound intensity techniques, NAH, and most time and frequency analysis methods can provide only the location and power of noise sources but cannot present details regarding the causes of undesirable noises or methods with which to modify them. Furthermore, due to the tightening of standards and the evolution of market requirements, simply recognizing the sources of noise may be insufficient to remedy vehicle interior noise. Although TPA can provide the contributions and transfer paths of noise sources, no specific method for optimizing those noise sources has been suggested. Generally, the improvement of a vehicle’s NVH after source identification is based mainly on trial and error and accumulated experience. Therefore, to overcome the aforementioned shortcoming, an effective and generalized method for

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identifying and optimizing the sources of a vehicle’s NVH is desired. In practice, the D&T of the sources of a vehicle’s NVH is equivalent to target cascading within a system. The key information learned during the D&T process that quantifies the intervals of the sources and their paths is also fundamental for developing methods with which to address this issue. This can be performed through target cascading, where system-level targets are backed up through the system to identify component-level targets and eventually to establish component-level D&T specifications based on those intervals. On this basis, this paper proposes a generalized inverse cascade method (GICM), which combines the systems engineering method and interval optimization technique to identify and optimize sources of vehicle interior noise. This approach is effectively suited for complex vibro-acoustic problems because it allows a multiple-input-single/multiple-output system to be broken down into cascade systems with feasible intervals given a wealth of D&T information. In this paper, a Volkswagen sedan is taken as an example to validate the proposed method. The remainder of this paper is organized as follows. In Section 2, the GICM method is proposed, and the process of identifying and optimizing the sources of vehicle interior noise is described. In Section 3, a noise source cascade tree is developed, and measurements are conducted. In Section 4, the main noise sources of a vehicle are identified, optimized and verified through the proposed GICM. Section 5 presents the conclusions.

2. The proposed method 2.1 Generalized inverse cascade method (GICM) Vehicle interior noise is complex, and its characteristics are based on the many physical structures of the system and components. As a result, interior noise and its sources exhibit broad coverage and low

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correlation. The GICM is proposed as an inverse numerical decision analysis method to quantify the decision process with alternative feasible intervals. The GICM uses systems engineering methods and the interval optimization technique to ultimately identify and optimize vehicle noise sources. The application of GICM to a decision problem involves the following three steps: (1) constructing the decision problem as a cascade tree; (2) developing a numerical model to quantify the cascade tree; and (3) solving the numerical model using the interval optimization method. These steps are detailed below. (1) Constructing the decision problem as a cascade tree. The systems engineering method, which is useful for developing targets at both the overall level and the subsystem level, can be leveraged to improve most product development processes for improving the noise and vibration performance. Vehicle interior noise and its sources are hierarchical and thus can be represented by a multilayer multiple-input-single-output (MISO) system, as shown in Fig. 1. The topmost layer, which constitutes the focus of the problem, is related to vehicle-level targets, which can be subjective or objective criteria of noise and vibration. The intermediate layers, which represent the interfaces of information interactions, include vehicle system-level and subsystem-level targets, which significantly influence vehicle interior noise. The bottom layer contains design variables and refers to component-level targets, which can be regarded as the influencing factors that contribute to the higher layers. It should be noted that the targets of a relatively higher layer can also be decomposed into cross layers; for example, the targets of layer 1 can be directly decomposed into the targets of layer 3 or layer 4, and the targets of layer 2 can also be directly decomposed into the targets of layer 4.

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Model 1 y Layer 1 Model 2 x1

x11

x12

Model 4

Model 3

x3

x2

x13

x21

x2 2

x2 3

x31

x32

Layer 2

x3 3

Layer 3

Layer 4

Fig. 1. Topological structure of a cascade tree.

(2) Developing a numerical model to quantify the cascade tree After constructing the abovementioned cascade tree, the next step is to quantify the abstract structure using a numerical model. In the cascade tree shown in Fig. 1, the targets of the bottom layer (layer 4) are the design variables, and the connected targets of the next higher layer (layer 3) are the design objectives, which are the design variables of the connected targets of a further, still higher layer (layer 2). Through this layerwise feedforward process, the target performance of the topmost layer can be synthesized and predicted. The numerical model for the cascade tree is defined as follows:

min. s. t.

ym(i -1) = f m(i −1) ( x1(i ) , x2(i ) ,..., xn(i ) ) , i = 2,3,..., I hk ( i ) ( x (i ) ) = 0, k = 1, 2,..., K g j (i ) ( x ( i ) ) ≤ 0, j = 1, 2,..., J P( lm(i −1) ≤ α ym( i −1) ≤ um(i −1) ) ≥ λm(i −1) ln( i ) ≤ xn( i ) ≤ un( i ) , n = 1, 2,..., N lm(i −1) ≤ ym(i −1) ≤ um(i −1) m = 1, 2,..., M

8

(1)

()

where


()

()

()

is the design objective of layer (i-1),  ,  , … , 

are the design variables of layer i,

and the kriging model is introduced as f, a nonlinear design objective function of the design variables, which will be described in the next subsection. N and M are the numbers of design variables and design objectives, respectively. hk and gj are the kth equality constraint and jth inequality constraint, respectively. J and K are the numbers of equality constraints and inequality constraints, respectively. P is a probabilistic operator, and (0 ≤ ≤ 1) is a predetermined satisfaction level.  is a conservative factor, and l and u are the lower and upper bounds, respectively, of the variables (layer i) and objectives (layer i-1). Note that, in contrast to the classic optimization method, the design objectives in Eq. (1) are not certain singular or scalar values; instead, each is a vector of discrete values within a reasonable interval. This substitution is implemented because, in practice, expanding the feasible interval of the design objectives has the advantage of reducing the difficulty of both design and manufacturing; furthermore, the uncertainty in actual operation processes can be tolerated. Similarly, this approach is also expected to reasonably expand the feasible interval of the design variables within the constraints. However, in a multilayer cascade system, this expansion would be restrained by the relevance between variables, which is characterized by the unity of opposites. A specific method should therefore be proposed to solve this model.

(3) Solving the numerical model using the interval optimization method Eq. (1) describes an uncertain optimization problem. Thus, it is necessary to transform this uncertain optimization problem into a certain optimization problem. Considering that an interval can be represented by the midpoint of the interval and a radius, expanding the interval is thus equivalent to minimizing the radius of the interval. Thus, the objective in Eq. (1) can be rewritten as follows:

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{ ym( i −1) } = min{vm(i −1) ( x1(i ) , x2(i ) ,..., xn(i ) ), wm( i −1) ( x1(i ) , x2(i ) ,..., xn(i ) )}, i = 2,3,..., I 1 L (i ) ( i ) ( f m ( x1 , x2 ,..., xn(i ) ) + f mR ( x1(i ) , x2(i ) ,..., xn(i ) )) 2 1 wm( i −1) ( x1(i ) , x2(i ) ,..., xn(i ) ) = ( f mR ( x1(i ) , x2(i ) ,..., xn(i ) ) − f mL ( x1(i ) , x2(i ) ,..., xn( i ) )) 2

vm(i −1) ( x1(i ) , x2(i ) ,..., xn(i ) ) =

(2)

where

f mL ( x1( i ) , x2( i ) ,..., xn( i ) ) = min( f m( i −1) ( x1( i ) , x2( i ) ,..., xn( i ) ))

(3)

f mR ( x1( i ) , x2( i ) ,..., xn( i ) ) = max( f m( i −1) ( x1( i ) , x2( i ) ,..., xn( i ) ))

In Eq. (2), the objective functions v and w represent the centers and radii, respectively, of the optimal interval under different conditions. The min{·} operation denotes finding the minimum value of each constituent element, and this is a multi-objective optimization problem.  and  shown in Eq. (3) denote the lower and upper bounds of the interval, respectively, and min[·] and max[·] denote the single objective optimization problem. These two objective functions may conflict with each other, and hence, a trade-off between them is necessary. Using a linear combination method to integrate these two objective functions as an assessment function is a relatively easy and convenient approach that has been widely applied to many types of engineering problems. In addition, by combining Eqs. (1)-(3) and applying the penalty function method to address the constraints, a certain optimization function is obtained as follows:

min.

ym( i −1) = β (vm( i −1) ( x1( i ) , x2( i ) ,..., xn( i ) ) + ξ1 ) / φ + (1 − β )( wm( i −1) ( x1(i ) , x2( i ) ,..., xn( i ) ) + ξ 2 ) / ϕ + I −1

J

K

+γ ∑ψ (P( lm( i −1) ≤ α ym( i −1) ≤ um( i −1) ) − λm ) + γ ∑ψ (- g j (i ) ( x ( i ) ))+γ ∑ψ (-hk ( i ) ( x ( i ) )) (4) i =1 j =1 k =1 s.t.

ln( i ) ≤ xn( i ) ≤ un( i ) , n = 1, 2,..., N lm( i −1) ≤ ym( i −1) ≤ um( i −1) m = 1, 2,..., M

where  (0 ≤  ≤ 1) is a weight coefficient used to make trade-offs between the two objective functions; most of the time,  = 0.5 is selected.  and  are constants that make the values within the brackets nonnegative.  and  are normalized factors; here,  = min (!) a nd  = min (")

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are selected. # is a penalty factor and is usually specified as a large value. The function $ is defined as follows:

ψ ( x) = (max(0, − x))2

(5)

Obviously, the function $ can adjust the penalty item according to the desired extent of the constraints. Finally, Eq. (4) can be solved through the classic optimization method.

2.2 Kriging model A vehicle’s NVH cascade targets and the vibro-acoustic transfer process are complex and nonlinear; hence, it is difficult and time consuming to develop a precise numerical model for a vehicle. To reduce the computation time required for the noise source identification and optimization process, the kriging model is introduced in this study. The kriging model is a nonparametric interpolation model for integrating given sample points to approximate the model parameters and for forecasting the unknown response of a new design point [21]. Given an m-dimensional vector x (m design variables) with n samples, the present kriging model expresses the unknown function y(x) as

y( x) = β + Z ( x)

(6)

where  is a constant global model, and Z(x) is the realization of a stochastic process with zero mean and variance % . The sample points are interpolated with a correlation function to estimate the trend of the stochastic processes. The correlation function between Z( ) and Z(& ) is strongly related to the distance D between sample points  and & , which can be expressed as k

D( xi , x j ) = ∑θ p xip − x jp

αp

(7)

p =1

where '( is the pth element of the correlation vector parameter ', and ( is the pth element determined by the correlation functions. Using the distance D, the entry correlation matrix R, which is an ) × ) matrix for Z(x), is defined as 11

R =Corr[ Z ( xi ), Z ( x j )] = exp[ −σ 2 D ( xi , x j )]

(8)

where Corr[·] is the correlation operation. The kriging predictor can be given as

y ( x ) ' =β ' +r T ( x ) R −1 ( y -aβ )

(9)

where ′ is the estimated value of , r(x) is the correlation vector between the prediction point x and the design points  , i=1, 2, …, n, y is the column vector of the response, and a is a unit vector with a length of n. The unknown parameter to construct the kriging model is ' , which can be estimated by maximizing the likelihood function:

1 1 L(β ', σ 2 ',θ ) = - [n ln(2π ) + n ln σ 2 + ln(R)+ 2 (y − aβ )T R −1 (y − aβ )] 2 2σ

(10)

For a given ', the terms ′ and % ′ can be estimated as follows:

β ' =[aT R -1a]−1 aT R -1y 1 n

σ 2 ' = (y − aβ ')T R −1 (y − aβ ')

(11) (12)

2.3 The process of identifying and optimizing vehicle interior noise sources The process used in this paper for identifying and optimizing vehicle noise sources using the GICM is shown in Fig. 2 and includes the following four steps. (1) Data acquisition The noise problem should be stated first to establish a general assessment of the interior noise. Then, the vehicle’s NVH cascade targets are decomposed in a layerwise fashion from the vehicle level to the system level, subsystem level and component level to develop and trim a cascade tree composed of vehicle noise sources. Based on this NVH cascade tree, the vehicle working conditions are selected, and noise and vibration measurements are acquired.

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(2) Signal processing An understanding of the characteristics of the vehicle noise and vibration signals makes it possible to locate those noise sources and make design changes. Accordingly, the interior noise and vibration signals are analyzed, and their characteristics are extracted.

(3) Noise source identification Based on the collected noise and vibration signals and their extracted characteristics, parametric models are developed using the kriging method to digitize the cascade tree of vehicle noise sources. Then, the vehicle noise sources are identified through the GICM.

Data acquisition

Noise source identification Problem statement

Develop the surrogate model using the kriging method

Develop and trim the cascade tree of vehicle noise sources Vehicle-level targets

NVH cascade targets

Sys tem-level targets Sub-systemlevel targets Componentlevel targets

Identify the vehicle noise sources using the GICM

Select operation conditions

Noise source optimization and verification Noise and vibration measurement Obtain the feasible intervals of noise sources

Signal processing Analyze interior noise and vibration

Optimize the vehicle interior noise

Extract noise source feature

Verify the proposed method

Fig. 2. Flow diagram of the identification and optimization of vehicle interior noise sources.

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(4) Noise source optimization and verification The GICM can also provide feasible noise source intervals, which can help in both the modification of design parameters and the optimization of noise sources. A verification test to validate the effectiveness of the proposed method is reported later in this paper.

3. Development of the cascade tree and measurement acquisition 3.1 Hierarchy of interior noise sources To improve the noise and vibration performance of a vehicle requires a full understanding of the vehicle system, can be obtained through the collection of data. In general, vehicle interior noise can be classified into airborne noise and structure-borne noise. Considering the sources of noise and vibration, these two categories of noise can be decomposed into system and subsystem noises, such as tire noise, engine noise, and suspension vibration noise, which represent the main sources of noise emanating from a vehicle. Some of these noise sources can become dominant under certain working conditions. Considering the influencing factors, these noise sources can even be decomposed into component-level targets, such as the rearview mirror, tire pressure, and shock absorber damping. These component-level targets may not generate noise directly, but their parameters will affect the noise and vibration of the overall system and its subsystems. Through decomposition, a hierarchical system of vehicle interior noise sources is obtained, as shown in Fig. 3, and constitutes the foundation for the development of a noise source cascade tree.

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Vehicle interior noise (airborne noise and structure-borne noise)

Vehicle level Wind noise System and subsystem level

Exhaust noise

Suspension vibration noise

Engine vibration noise

Component level

Transmission noise

Engine noise

Tire noise

Subframe vibration noise

Exhaust pipe vibration noise

Rearview mirror

Windshield wiper Wheel casing

Tire pressure

Tire ripple

Combustion noise

Induction noise Gear meshing noise

Bushing stiffness

Bearing noise

Spring stiffness

Muffler transmission loss

Road surface roughness

Mount stiffness

Drive shaft noise Insertion loss

Shock absorber damping

Lug stiffness

Fig. 3. The hierarchical system of vehicle interior noise sources.

3.2 Developing and trimming the noise source cascade tree Through hierarchical decomposition, a complete noise source cascade tree can be established that includes three levels: the vehicle level, the system and subsystem level, and the component level. However, in practice, a large number of noise sources exist within a vehicle, and a complex noise source cascade tree would complicate the identification process, thereby increasing the computation time. Fortunately, it is not necessary to identify all the noise sources, because the main emphasis should be placed on the potential main noise sources. For a vehicle, a subjective evaluation could narrow down the number and regions of potential noise sources both efficiently and effectively. Therefore, a preliminary subjective evaluation is introduced to trim the noise source cascade tree. Fig. 4 shows a 7-scale rating method for a subjective evaluation of vehicle interior noise in which a higher score represents a better perception of interior noise. This method, which can provide an overall estimation of interior noise, is recommended by the China Automotive Technology & Research Center, Tianjin, China.

15

Excellent

Good

Acceptable

Marginal

7

Not good

Bad

Unacceptable

1 Rating scale

Fig. 4. Subjective rating scale and score range.

A Volkswagen sedan with front wheel drive was used as an example for the identification of interior noise sources in this study. An in situ subjective evaluation was performed by automotive engineers to assess the interior noise of the vehicle. The sample vehicle was tested on a straight concrete road. During the experiment, the heating, ventilation and air conditioning (HVAC) system was off, and the windows were closed. Five different working conditions were considered in the tests, and the corresponding subjective ratings and descriptions shown in Tab. 1 were obtained according to Fig. 4. In an idling state, the vehicle interior noise was perceived as excellent by both the driver and the passenger, which means that the vehicle initial state was good. However, when the vehicle was driven at a slow speed (<50 km/h), the perception of the interior noise became less favorable, especially regarding abnormal noise originating from the lower front portion of the vehicle at a vehicle speed of 30 km/h. As the vehicle speed increased, the abnormal noise was masked by the engine noise, wind noise and other noises. People are more sensitive to abnormal noise when a vehicle is driving at low speed because the background noise is low, and people have high expectations of the interior noise environment [22,23]. This result illustrates that although an abnormal noise may not be loud, such a sound could decrease the interior sound quality and negatively affect the psychological perception of passengers. When the vehicle was driven at a sped exceeding 50 km/h, engine noise, tire noise and exhaust noise were the main noise sources. Wind noise, engine noise and transmission noise became dominant after the vehicle reached a speed higher than 100 km/h; however, these noises were not as psychologically annoying as 16

the abnormal noise perceived at a lower speed. The perception of interior noise during a coasting state was consistent with that during a driving state.

Tab. 1 Working conditions and preliminary evaluation of vehicle interior noise. Index

Working conditions

Description

Score

#1

Idling state

The interior noise is excellent.

7

#2

Slow speed

The interior noise is bad, especially the abnormal noise coming from the

2

(< 50 km/h)

front-lower area of the vehicle when driving at 30 km/h on rough roads.

Medium speed

The interior noise is good. The engine noise, tire noise and exhaust noise

(50 km/h - 100 km/h)

are the main noise sources but are not prominent.

Fast speed

The interior noise is marginal. The wind noise, engine noise and

(100 km/h - 140 km/h)

transmission noise are the dominant sources but are not annoying.

Coasting state (engine

The interior noise is acceptable, but the abnormal noise coming from the

off, 140 km/h - 0 km/h)

front-lower area of the vehicle at a speed of 30 km/h is annoying.

#3

#4

#5

6

4

4

According to the subjective evaluation provided above, the vehicle-level target of the noise source cascade tree is the abnormal noise originating from the front-lower portion of the vehicle. Because this abnormal noise was heard at a low vehicle speed (30 km/h), wind noise can be eliminated. This specific noise also occurred during a coasting state, which implies that engine noise is not the abnormal noise source. Considering the area from which the abnormal noise originates, tire noise, transmission noise, front subframe vibration noise, front suspension vibration noise, and engine mount vibration noise are the potential noise sources and are hence regarded as the system/subsystem-level targets of the noise 17

source cascade tree. According to the influencing factors analyzed in the hierarchical system shown in

Fig. 3, the component-level targets of the noise source cascade tree can be determined. Since the direct influencing factors of transmission noise, such as gears and bearings, are difficult to modify in practice, the transfer path, i.e., the acoustic absorptivity and acoustic insulation power of the cowl panel, is introduced as an indirect influencing factor. Combined with the preliminary subjective evaluation and construction of the vehicle, a final trimmed interior noise source cascade tree is consequently developed, as shown in Fig. 5.

Abnormal interior noise

Tire noise

Transmission noise

Subframe vibration noise

Suspension vibration noise

Engine mount vibration noise

Fig. 5. Cascade tree of interior noise sources.

3.3 Noise and vibration measurements By trimming the cascade tree of interior noise sources based on the subjective evaluation, the potential noise sources were narrowed down and preliminarily determined. Next, to build the GICM numerical model and calculate the feasible intervals for the identification and optimization of interior noise sources, noise and vibration data were obtained. A detailed measurement scheme was implemented to collect noise and vibration signals. The layout of the test vehicle is shown in Fig. 6. 18

According to the standard GB/T 18697 [24], the interior noise above the driver’s seat was recorded using a G.R.A.S.40HF microphone, which was 0.75 m from the floor and 0.25 m away from the centerline of the seat, as shown in Fig. 7(a). To record potential airborne noises, one microphone with a wind cover was mounted 0.2 m away from the front tire on the wheel casing and 0.3 m above the ground, as shown in Fig. 7(b). Transmission noise was measured using one microphone with a wind cover mounted behind the transmission with a gap of 0.2 m, as shown in Fig. 7(c). Structure-borne noise was measured using the reference signal of the vibration acceleration to approximate its intensity and characteristics [25,26]. Accordingly, accelerometers were mounted on the panels of the car body and connected to the subframe, suspension and engine mounts to quantify subframe vibration noise, suspension vibration noise and engine mount vibration noise, respectively, as shown in Fig. 7(d)-(f). These accelerometers were placed in the normal direction of the panel vibration. Because the structural parameters of the tires, subframe and suspension are symmetric, the noise and vibration for the left and right sides of the vehicle are similar. Thus, the noise and vibrations on the left side of the vehicle were selected for measurement. The abnormal interior noise mentioned above may have been caused by parameter mismatch among suspension components. To identify the interior noise sources and conduct the optimization, the original vehicle status and several fine-tuned vehicle statuses, including component parameters that were modified according to Fig. 5, were measured in this study. The original vehicle component parameter is regarded as the baseline status, and the two modified statuses of the component parameters denoted “1” and “2” are shown in Tab. 2. Specifically, the baseline road is the concrete pavement, while the roads of statuses “1” and “2” are a stone road and an asphalt road, respectively. Three cowl panel materials, including the baseline status with different acoustic absorption coefficients and acoustic

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reduction coefficients, were used. For convenience, the tire pressure, shock absorber damping and rubber stiffness parameter values of statuses “1” and “2” were upregulated by 20% and downregulated by 20%, respectively, relative to the corresponding baseline values. Because the excitation force mainly originates from the vehicle’s vertical direction, only the Z-axis rubber stiffness in the vehicle coordinate system (see Fig. 6) was changed. In addition, to construct a more rational relationship between the noise sources and component design variables, only the component parameters of one branch in the noise source cascade tree (Fig. 5) were modified in each experiment. The other 4 branches remained at the baseline. Tab. 3 shows the statuses corresponding to the selection of parameters presented in Tab. 2. For example, in the tire noise branch, the road surface roughness and tire pressure were combined in five different ways according to Tab. 3, and each combination was measured independently, while the other 4 branches retained their original statuses. This process was implemented for all five branches successively, and a total of 21 measurements were performed. A constant speed of 30 km/h was selected. All acoustical and vibrational signals were recorded simultaneously. The data were collected using a Siemens LMS SM32 data acquisition system and saved on a mobile workstation. To reconstruct the interior noise, a signal length of 10 s and a sampling rate of 40 kHz were applied. Structure-borne energy was distributed mainly in the low- and middle-frequency bands, and a sampling rate of 4 kHz for the vibration signals was considered acceptable in this study.

20

Suspension Engine Z

Transmission Y

X

Subframe

Transmission Y

Subframe Z

Engine Suspension

Fig. 6. Sketch of the vehicle cabin.

21

X

(a)

(b)

Microphone Microphone with wind cover

(d)

(c)

Microphone with wind cover beside the transmission

Accelerometer on the subframe panel

(f)

(e)

Engine mount

Accelerometer on the suspension panel

Accelerometer on the engine mount panel

Fig. 7. Setup of noise and vibration measurement sensors within the vehicle cabin.

22

Tab. 2 Baseline and fine-tuned states of the component parameters. No.

Component name

Baseline “0”

Status “1”

Status “2”

#1

Road surface roughness (m-3)

7.61

15.23

3.81

#2

Tire pressure (bar)

2.3

2.7

1.9

#3

Cowl panel acoustic absorption coefficient

0.54

0.62

0.42

#4

Cowl panel acoustical reduction coefficient

0.62

0.73

0.54

#5

Left bush stiffness (kN/m)

780

930

620

#6

Front engine mount stiffness (kN/m)

90

110

70

#7

Spring stiffness (kN/m)

31

37

25

#8

Shock absorber damping (kNs/m)

2.5

3.0

2.0

#9

Left engine mount stiffness (kN/m)

340

400

270

#10

Right engine mount stiffness (kN/m)

410

490

330

Tab. 3 Component parameter combinations. Combination

Status of variable 1

Status of variable 2

Baseline

“0”

“0”

Condition 1

“1”

“1”

Condition 2

“1”

“2”

Condition 3

“2”

“1”

Condition 4

“2”

“2”

23

4. Results and discussion 4.1 Interior noise and vibration analysis The sound pressure spectra of the interior noise and nearfield noise from the transmission and tires are shown in Fig. 8. As illustrated in Fig. 8(a), the interior noise is low frequency up to 1000 Hz since a high noise source is blocked. In Fig. 8(b), the tire noise is wideband, and two dense energy bands of tire noise are observed: 200-400 Hz and 800-1000 Hz. Fig. 8(c) shows that transmission noise is also wideband up to 1000 Hz with a few peaks, and the noise energy fluctuated wildly throughout the entire frequency band. Although the SPLs of the airborne noise from the tires and transmission are higher than that of the interior noise, the cowl panel can absorb and insulate airborne noise energy, especially in the high-frequency band, and thus, only a portion of the airborne noise is transferred into the cabin. According to the interior noise and airborne noise sources, the main noise is concentrated at low-to-medium frequencies (20-1000 Hz). In addition to airborne noise, the measured structural vibrations attributable to structure-borne noise from the subframe, suspension, and left and right engine mounts are shown in Fig. 9. These spectra show that the vibration characteristics at each measurement point are different, thereby generating different structure-borne noises and potentially causing the abnormal interior noise. The vibration of the subframe panel was distributed mainly in the frequency band below 400 Hz with peaks at approximately 100 Hz and 240 Hz. The major energy of the suspension panel vibration was distributed within 0-500 Hz. Many peaks are observed in the suspension panel vibration because road vibrations are broadband and complex, and the damping characteristic of the shock absorber is nonlinear. The vibration caused by the left engine mount panel exhibits two peaks at 17 Hz and 33 Hz. On the other hand, the vibration caused by the right engine mount panel is characterized by three peaks at 16

24

Hz, 34 Hz and 53 Hz. These spectra show that the panel vibrations of the left and right engine mounts were concentrated mainly below 200 Hz because the vibration source of an engine mount is relatively simple. 80 60

(a)

40 20 0 -20 -40 20

2000

4000

6000

8000

10000

Frequency (Hz) 80

80

70

70

(b)

60 50

50

40

40

30

30

20

20

10 20

2000

4000

6000

8000

(c)

60

10 20

10000

Frequency (Hz)

2000

4000

6000

Frequency (Hz)

Fig. 8. SPLs at measurement points: (a) interior noise; (b) tire noise; (c) transmission noise.

25

8000

10000

1.5

3.5

(a)

(b)

3 2.5

1

2 1.5 0.5

1 0.5

0

0 0

100

200

300

400

500

0

100

Frequency (Hz)

200

300

400

500

Frequency (Hz)

0.3

0.5

(c)

0.25

(d) 0.4

0.2 0.3 0.15 0.2 0.1 0.1

0.05 0

0 0

100

200

300

400

500

0

Frequency (Hz)

100

200

300

400

500

Frequency (Hz)

Fig. 9. Vibration accelerations at measurement points: (a) subframe panel; (b) suspension panel; (c) left engine mount panel; (d) right engine mount panel.

Due to the complexity of vehicle interior noise, especially abnormal interior noise, it is difficult to accurately identify this specific noise source directly through traditional numerical methods. Consequently, a subjective evaluation is carried out to preidentify the noise sources. In this study, a high-quality Sennheiser HD 800 system was introduced to play back the recorded interior noise with high-pass filters, and the broadcast sounds were subjectively evaluated by fifteen people (8 males and 7 females with a mean age of 26 years and a standard deviation of 5.5 years) with normal hearing using the scale rating method shown in Fig. 4. Specifically, the original interior noise at the baseline vehicle status was postprocessed by octave-band high-pass filters, i.e., with low cutoff frequencies of 20 Hz, 26

31.5 Hz, 63 Hz, 125 Hz, …, 8000 Hz and the same bandwidth of 20,000 Hz. Accordingly, a total of 10 filtered interior noise signals were obtained and evaluated individually. The evaluation results were verified through concordance analysis [27]; the Kendall concordance coefficient was 0.812, which is greater than 0.6, and the significance level was 0.000, which means that the same standard was applied for the evaluations of all fifteen participants. Fig. 10 shows the mean subjective rating scores of the evaluators of the filtered interior noises. The rating scores were less than 4 when the filtered sounds included the frequency band of 20-500 Hz. However, when the low cutoff frequency was higher than 500 Hz, the rating scores improved gradually and reached a score of 6.3 in the evaluation of the frequency band of 8000-20000 Hz. This result illustrates that the abnormal interior noise was contained mainly in the frequency band below 500 Hz, which is consistent with the objective analysis results displayed in Fig. 8 and Fig. 9. Due to the close relationship between the vehicle interior noise and component parameters, the abnormal interior noise may have been caused by mismatched component parameters. The above analysis reveals that the abnormal interior noise was contained in the frequency band of 20-500 Hz. Therefore, the SPLs between 20 and 500 Hz of the interior noise were calculated under the 21 test conditions (a combination of Tab. 2 and Tab. 3, as described in Section 3.3), and their corresponding subjective evaluations… the results are shown in Fig. 11. The red curve in Fig. 11(a) represents modified components #1 (road surface roughness) and #2 (tire pressure) with the combination of 4 conditions (except the baseline) in Tab. 3; the other curves represent other component combinations accordingly. Changing the component parameters has different influences on the SPL of the abnormal interior noise. The SPL of the interior noise at the original baseline status in the 20-500 Hz range was 78.5 dB. Tests No. 2 (driving on a stone road with a tire pressure of 2.7 bar) and 14 (with a spring

27

stiffness of 37 kN/m and shock absorber damping of 3.0 kNs/m) have high interior noise SPLs of 80.8 dB and 81.0 dB, respectively, in the 20-500 Hz range. These values mean that the combination of a rough road surface with high tire pressure or the combination of a large spring stiffness with high shock absorber damping will increase the SPL of interior abnormal noise. Tests No. 6 (with a cowl panel acoustic absorption coefficient of 0.62 and a cowl panel acoustical reduction coefficient of 0.73) and 15 (with a spring stiffness of 37 kN/m and a shock absorber damping of 2.0 kNs/m) have low interior noise SPLs of 74.2 dB and 72.7 dB, respectively, in the 20-500 Hz range. Therefore, increasing the absorption and reduction characteristics of the cowl panel will improve the perception of interior noise. In addition, an appropriate match of the suspension stiffness and damping can obtain satisfactory interior noise SPLs and eliminate abnormal noise. The interior noise at the original baseline status contained abnormal noise in the subjective evaluation, which illustrates that an interior noise SPL exceeding 78.5 dB in the 20-500 Hz range would weaken the interior sound quality. In fact, as shown in Fig. 11(a) and (b), an interior noise SPL exceeding 76.5 dB in the 20-500 Hz range resulted in a subjective rating lower than 4, which means that the perception of the noise is below “Marginal” according to Fig. 4. In other words, interior noise SPL higher than 76.5 dB in the 20-500 Hz range has the characteristics of abnormal noise, but an SPL lower than 76.5 dB does not exhibit the characteristics of abnormal noise. Based on Fig. 11, test No. 15 performed the best, i.e., it had the lowest SPL and highest rating score of interior noise in the 20-500 Hz range. Fig. 12 shows the measured noise and vibration signals under the conditions of this test. The noise and vibration trends of test No. 15 are similar to those for the vehicle baseline status. The main energies of the interior noise, airborne noise and structure vibrations are distributed at low and medium frequencies. Moreover, it is clear that the noise and vibration energies of the spectra below 500 Hz are

28

different between the status of test No. 15 and the baseline status, especially at the subframe panel and suspension panel positions. To illustrate the distinction more clearly, Tab. 4 presents the SPLs and root mean squares (RMSs) of the noises and vibrations below 500 Hz for comparison. Evidently, the SPL of interior noise was decreased by nearly 6 dB from the baseline status to test No. 15. The vibration RMSs of the subframe panel and suspension panel decreased from 0.51 m/s2 to 0.44 m/s2 and from 1.09 m/s2 to 0.61 m/s2, respectively. The other noise and vibration RMSs of the reference components were also changed, but not prominently. From the above analysis, the abnormal interior noise is structure-borne noise caused by the vibrations of the subframe panel and suspension panel. Therefore, the GICM appears to accurately identify the noise source.

Fig. 10 Subjective evaluation scores of the filtered vehicle interior noise.

29

84

(a)

82 80

Base line Modified components #1 & #2 Modified components #3 & #4 Modified components #5 & #6 Modified components #7 & #8 Modified components #9 & #10

78 76 74 72 70 0

5

10

15

20

Test serial number 7

(b)

6 5 4 3 2 1 0

5

10

15

20

Test serial number Fig. 11. Interior SPLs at the driver’s right ear position under different test conditions.

30

Sound pressure level dB (2 10 -5Pa)

80

(a) 60

40

20

0

-20 20

2000

4000

6000

8000

10000

Frequency (Hz) 80

(b)

70

Sound pressure level dB (2 10 -5Pa)

Sound pressure level dB (2 10 -5Pa)

80

60 50 40 30

(c)

70 60 50 40 30 20

20 10 20

2000

4000

6000

8000

10 20

10000

2000

4000

6000

8000

10000

Frequency (Hz)

Frequency (Hz) 3.5

1.5

(e)

3

(d)

2.5 1 2 1.5 0.5

1 0.5 0

0 0

100

200

300

400

0

500

100

200

300

400

500

Frequency (Hz)

Frequency (Hz) 0.3

0.5

(f)

0.25

(g)

0.4

0.2 0.3 0.15 0.2 0.1 0.1

0.05 0

0 0

100

200

300

400

500

0

Frequency (Hz)

100

200

300

400

500

Frequency (Hz)

Fig. 12. SPLs and vibration accelerations at measurement points: (a) interior noise; (b) tire noise; (c) transmission noise; (d) subframe panel; (e) suspension panel; (f) left engine mount panel; (g) right engine mount panel. 31

Tab. 4 SPLs of the noise (20-500 Hz) and RMSs of the vibration (0-500 Hz) spectra of the baseline and test No. 15. Position

Baseline

Test No. 15

Interior noise (dB)

78.5

72.7

Tire noise (dB)

85.4

84.8

Transmission noise (dB)

84.5

84.0

Subframe panel vibration (m/s2)

0.51

0.44

Suspension panel vibration (m/s2)

1.09

0.61

Left engine mount panel vibration (m/s2)

2.5×10-2

2.8×10-2

Right engine mount panel vibration (m/s2)

3.1×10-2

3.2×10-2

4.2 Identifying noise sources using the GICM Figs. 8 and 12 clearly show that the interior noise energy is dominant at low and middle frequencies. The major purpose of this paper is to identify and optimize the potential sources of abnormal interior noise at low and medium frequencies. As described in Section 2.2, after the cascade tree is constructed, the next step is to develop a numerical model to quantify the cascade tree and then solve the numerical model using the interval optimization method. According to the constructed cascade tree shown in Fig. 5, level 1 is the abnormal interior noise, and level 2 contains five potential system/subsystem-level noise sources. With level 1 as the design objective and level 2 as the design variables, the feasible interval of each design variable can be calculated through the GICM. The numerical model represented by Eq. (13) between cascade tree levels 1 and 2 is developed using Eq. (1) as follows:

32

min.

y1(1) = f1(1− 2) ( x1(2) , x2(2) ,..., xn(2) ) P( l1(1) ≤ α y1(1) ≤ u1(1) ) ≥ λ1(1)

s. t.

(13)

ln(2) ≤ xn(2) ≤ un(2) , n = 1, 2, ..., 5 l1(1) ≤ y1(1) ≤ u1(1) ()

where


( )

is the interior SPL in the 20-500 Hz range,  ( )

( )

transmission noise, respectively, and , , -

( )

and .

( )

and 

are the SPLs of tire noise and

are the panel vibration RMSs of the subframe, ( )

suspension and engine mount (mean of left and right), respectively, in the 20-500 Hz range. 

is a

kriging model that develops a nonlinear mapping relationship between levels 1 and 2 in the cascade tree. From the subjective evaluation and experimental results, an interior noise SPL exceeding 76.5 dB in the 20-500 Hz range would lead to the perception of annoyance caused by the abnormal noise. Therefore, ()

()

()

()

the upper bound of
 , i.e., / , is set to 76.5 dB, and the lower bound of
 , i.e., 0 , could be set to a low value. In this study, the lowest interior noise SPL (72.7 dB) in the 20-500 Hz range among ()

the 21 experiments was selected as 0 . Similarly, the highest and lowest SPLs and the vibration RMSs of the five potential noise sources in the 21 experiments were selected as the upper bound and lower ( )

( )

( )

( )

( )

bound of the design variables, i.e., [0 , 0 , 0, , 0- , 0. ] = [82.5, 81.7, 0.42, 0.61, 2.80] and ( )

( )

( )

( )

( )

[/ , / , /, , /- , /. ] = [88.6, 88.0, 0.55, 1.35, 3.15]. To obtain a robust result, the conservative ()

factor  was introduced and set to 1.05. The predetermined satisfaction level 

was set to 1 for the

most satisfactory solution. Using the interval optimization method proposed in Section 2.2, the uncertain optimization function of Eq. (13) can be transformed into a certain optimization function as follows:

min.

y1(1) = β (v1(1−2) ( x1(2) , x2(2) ,..., xn(2) ) + ξ1 ) / φ + (1 − β )(w1(1−2) ( x1(2) , x2(2) ,..., xn(2) ) + ξ2 ) / ϕ + +γψ (P( l1(1) ≤ α y1(1) ≤ u1(1) ) − λ1(1) )

s.t.

(14)

ln(2) ≤ xn(2) ≤ un(2) , n = 1, 2,...,5 l1(1) ≤ y1(1) ≤ u1(1)

where the weight coefficient  is set to 0.5 as a compromise between the center and the radius of the 33

interval. Since the radii of the optimal intervals v and w are positive, the constants  and  were set to 0. The normalized factors  = min (!) and  = min (") are used to make the solution converge, and a large penalty factor # = 1000 is selected to ensure the constraint conditions. The certain optimization function in Eq. (14) can be solved through traditional methods; the calculated feasible intervals of the five design variables are shown in Tab. 5. The SPLs and vibration RMSs of the baseline values are within the feasible intervals, except for the vibration RMS of the suspension vibration panel at 1.09 m/s2, which is higher than the upper bound of 0.92 m/s2. The results show that the tire noise, transmission noise, and structure-borne noises of the subframe and engine mount are not the major sources of the abnormal interior noise, whereas the structure-borne noise of vibration generated from the suspension probably represents the abnormal interior noise source. Therefore, it is necessary to reduce the suspension panel vibration to decrease the structure-borne abnormal noise.

Tab. 5 Calculated feasible intervals of the noises and vibrations of the five subsystems. No.

System-level parameters

Baseline value

Lower bound

Upper bound

#1

Tire noise (dB)

85.4

82.5

87.3

#2

Transmission noise (dB)

84.5

81.7

86.9

#3

Subframe vibration (m/s2)

0.51

0.42

0.53

#4

Suspension vibration (m/s2)

1.09

0.61

0.92

#5

Engine mount vibration (m/s2)

3.11×10-2

2.80×10-2

3.15×10-2

34

To further investigate the source of the suspension panel vibration RMS that exceeds the upper bound of the feasible interval, the GICM is applied to develop the relationship between levels 2 and 3 in the cascade tree. Generally, in this study, five numerical models were developed for each system branch through Eq. (1), as follows:

ym(2) = f m(2 −3) ( x1(3) , x2(3) ) , m = 1, 2,...,5

min. s. t.

P( lm(2) ≤ α ym(2) ≤ um(2) ) ≥ λm(2)

(15)

ln(3) ≤ xn(3) ≤ un(3) , n = 1, 2 lm(2) ≤ ym(2) ≤ um(2) ( )

where the design objectives
 , 3 = 1,2, … 5, are the SPLs and vibration RMSs of the five systems in (,)

the 20-500 Hz range, 

(,)

and 

( ,)

are the corresponding design variables of each system, and 

are the kriging models that map the relationships of the branches between levels 2 and 3 in the cascade ( )

( )

tree. 0 and / are the lower bound and upper bound, respectively, of the mth design objective set (,)

as the calculated bounds in Tab. 5 for each system. Similarly, 0

(,)

and / , ) = 1,, are the lower

bound and upper bound, respectively, of the design variables set as the values of statuses “1” and “2” in ( )

Tab. 2. The conservative factor is  = 1.05, and the satisfaction level is  = 1, 3 = 1,2, … 5. The uncertain optimization function of Eq. (15) can be transformed into a certain optimization function as follows:

min.

ym(2) = β (v1(2−3) ( x1(3) , x2(3) ) + ξ1 ) / φ + (1 − β )( w1(2−3) ( x1(3) , x2(3) ) + ξ 2 ) / ϕ + +γψ (P( lm(2) ≤ α ym(2) ≤ um(2) ) − λm(2−3) ), m = 1, 2,...,5

s.t.

(16)

ln(3) ≤ xn(3) ≤ un(3) , n = 1, 2 lm(2) ≤ ym(2) ≤ um(2)

where the weight coefficient is  = 0.5 as a compromise between the center and the radius of the interval, the constants are set to  =  = 0 , the normalized factors are  = min (!) and  = ( ,)

min ("), and the penalty factor is set to # = 1000. Since each kriging model 

, m=1,2,…,5, has

a 2-D design variable, 3-D visual plots of the developed kriging models of the tire noise, transmission 35

noise, subframe panel vibration, suspension panel vibration and panel engine mount vibration are shown in Fig. 13. The middle point on each plot surface represents the vehicle baseline status, while the other 4 points along the surface edges represent the modified vehicle statuses. The calculated feasible intervals of the design variables of the five systems are shown in Tab. 6 through Tab. 10. Based on these results, to control the tire noise within [82.5, 87.3] dB, the road surface roughness should be in the range of [3.81, 10.24] m-3, and the tire pressure should be in the range of [1.90, 2.70] bar. The baseline values of the road surface roughness and tire pressure were 7.61 m-3 and 2.3 bar, which did not exceed the lower and upper bounds of the feasible intervals. Consequently, the tire noise at the baseline status was 85.4 dB, which satisfies the design objective range of [82.5, 87.3] dB. In addition, the baseline values of the design variables of transmission noise, subframe panel vibration, and panel engine mount vibration were all within the calculated feasible intervals. Therefore, the baseline objective values of the transmission noise (84.5 dB), subframe panel vibration (0.51 m/s2), and panel engine mount vibration (3.11 m/s2) were within their calculated intervals. However, the shock absorber damping of the baseline status was 2.50 kNs/m, which is outside the upper bound (2.38 kNs/m) of the calculated feasible interval. As a result, the vibration RMS of the suspension panel (1.09 m/s2) exceeded the upper limit of the feasible interval (0.92 m/s2). This is the main reason for the structure-borne noise emanating from the suspension vibration that generates the abnormal interior noise.

36

0.55

0.5

0.45

0.4 120

100 Fron 80 t eng 60 600 ine m ount stiffn ess (N /m)

700

800

900

1000

(N/m) stiffness Left bush

3.2

1.4

3.1

1.2 3

1 2.9

0.8 2.8 500

0.6 3 2.5

Shoc k abs orber damp ing

2

(Ns/m )

25

30

40

35

fness Spring stif

(N/m)

400

Righ t

engi ne

300

250

350

400

mou nt st ss (N/m) iffne mount stiffne ss (N Left engine /m)

Fig. 13. Interpolation results of the kriging models between cascade tree levels 2 and 3.

37

300

Tab. 6 Feasible intervals of the design variables of the tire noise. No.

Component-level parameters

Baseline value

Lower bound

Upper bound

#1

Road surface roughness (m-3)

7.61

3.81

10.24

#2

Tire pressure (Bar)

2.30

1.90

2.70

Tab. 7 Feasible intervals of the design variables of the transmission noise. No.

Component-level parameters

Baseline value

Lower bound

Upper bound

#1

Cowl panel acoustic absorption coefficient

0.54

0.45

0.62

#2

Cowl panel acoustical reduction coefficient

0.62

0.58

0.73

Tab. 8 Feasible intervals of the design variables of the subframe panel vibration. No.

Component-level parameters

Baseline value

Lower bound

Upper bound

#1

Left bush stiffness (kN/m)

780

620

930

#2

Front engine mount stiffness (kN/m)

90

70

102

Tab. 9 Feasible intervals of the design variables of the panel suspension vibration. No.

Component-level parameters

Baseline value

Lower bound

Upper bound

#1

Spring stiffness (kN/m)

31

25

34

#2

Shock absorber damping (kNs/m)

2.50

2.00

2.38

38

Tab. 10 Feasible intervals of the design variables of the panel engine mount vibration. No.

Component-level parameters

Baseline value

Lower bound

Upper bound

#1

Left engine mount stiffness (kN/m)

340

270

400

#2

Right engine mount stiffness (kN/m)

410

330

490

4.3 Optimization and verification of the abnormal interior noise source To verify the proposed method, the shock absorber damping of the suspension system was modified according to the calculated feasible interval in Tab. 9. Without weakening the vehicle riding comfort or handling stability, a new shock absorber damping force of 2.30 kNs/m, which is within the feasible interval, was tuned by excluding one valve plate from the shock absorber piston, while the stiffness of the suspension spring and the other system components were kept at their corresponding baseline values. A vehicle road test was performed to validate the interior noise of the modified vehicle status, and a subjective evaluation was implemented. Fig. 14 compares the recorded interior noise and the suspension panel vibration in the baseline state and the modified state. Fig. 14(a) shows that the interior noise energy dominated at low frequencies, and the modified interior noise energy below 1500 Hz decreased compared with the baseline state. As shown in Fig. 14(b), the energy of the suspension panel vibration was distributed mainly at frequencies below 400 Hz and exhibited many peaks. Comparing the vibration spectra of the modified state with the baseline state shows a clear drop in the former vibration energy dropped. Fig. 15 shows the corresponding time-frequency spectra of interior noise and suspension panel vibration. The amplitudes of the modified interior SPL and suspension panel vibration both decreased. In addition, Tab. 11 presents the SPLs of the recorded noises and RMSs of the vibration spectra of the baseline and optimization statuses. Since only the shock absorber damping was

39

modified, the tire noise, transmission noise, subframe panel vibration and panel engine mount vibration exhibited only small changes. However, the vibration RMS of the suspension panel decreased from 1.09 m/s2 to 0.83 m/s2, which was in the range of the feasible interval [0.61, 0.92] m/s2. In addition, the interior SPL decreased from 78.5 dB to 74.7 dB, which was below the threshold of 76.5 dB that leads to abnormal interior noise. It is noted that 74.7 dB is not the best solution because in contrast to the traditional optimization methods, the design objective and design variables in the interval optimization method are intervals rather than singular values. Consequently, the calculated results are intervals. This can be regarded as a generalized optimization method that can provide many feasible solutions under the constraint conditions and target requirements. The “optimization” may not provide the best solution but does provide a feasible solution interval, which can improve design tolerance. The subjective evaluation score of the interior noise of the optimized status increased to 5.3, which means that the perception of interior noise was acceptable according to the subjective rating scale without the abnormal noise characteristic. Therefore, the optimized result for the vehicle interior noise was achieved, and the proposed GICM was validated.

Sound pressure level dB (2 10 -5Pa)

80 60

3.5 Baseline Modified

(a)

Baseline Modified

(b)

3 2.5

40

2 20 1.5 0

1

-20 -40 20

0.5 0 2000

4000

6000

8000

10000

Frequency (Hz)

0

100

200

300

Frequency (Hz)

Fig. 14 Sound pressure and vibration spectra: (a) interior noise; (b) suspension panel vibration.

40

400

500

Fig. 15 Time-frequency spectra of noise and vibration: (a) baseline interior noise; (b) modified interior noise; (c) baseline suspension panel vibration; (d) modified suspension panel vibration.

Tab. 11 SPLs of the noise (20-500 Hz) and RMSs of the vibration (0-500 Hz) spectra of the baseline and optimized statuses. Baseline

Optimization

(2.3/7.0)*

(5.3/7.0)*

Interior noise (dB)

78.5

74.7

Tire noise (dB)

85.4

85.1

Transmission noise (dB)

84.5

84.8

Subframe panel vibration (m/s2)

0.51

0.47

Suspension panel vibration (m/s2)

1.09

0.83

Left engine mount panel vibration (m/s2)

2.5×10-2

2.6×10-2

Position

41

Right engine mount panel vibration (m/s2)

3.1×10-2

3.0×10-2

*(Subjective evaluation score/max score)

5. Conclusion This paper proposes a generalized inverse cascade method (GICM), which combines systems engineering with the interval optimization technique to identify and optimize vehicle noise sources. A cascade tree of vehicle interior noise was constructed, and a vehicular road test was performed to collect the potential sources of interior noise. Through both objective and subjective evaluation, the abnormal interior noise of the tested vehicle was found to be distributed mainly in the 20-500 Hz frequency band. The interior noise SPL of the vehicle baseline status in the 20-500 Hz band was 78.5 dB, which is higher than the abnormal SPL threshold of 76.5 dB. Through the GICM, the feasible intervals of five system objectives were calculated, and the vibration RMS of the suspension panel in the 20-500 Hz band (1.09 m/s2) exceeded the upper bound of the feasible interval (0.92 m/s2). This is the main reason for the structure-borne abnormal noise generated by the vibration of the suspension panel. Moreover, the GICM was used to calculate the feasible intervals of the spring stiffness and shock absorber damping in the suspension system. The results showed that the damping force of the shock absorber (2.5 kN/m) is outside the range of the feasible interval (2.38 kN/m). Modifying the shock absorber damping force (to 2.3 kN/m) according to the calculated feasible interval reduced the vehicle interior SPL to 74.7 dB. Through a subjective evaluation, the vehicle interior noise was optimized, and the proposed GICM was validated.

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Acknowledgments This work was supported by the Chinese National Science Foundation Grant (No. 51905408, No. 51775451), the Shaanxi Province Science Foundation Grant (No. 2019JQ-040), the China Postdoctoral Science Foundation (No. 2018 M633497) and the Postdoctoral Science Foundation of Shaanxi Province.

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

A new method, the generalized inverse cascade method (GICM), is proposed.



The GICM combines systems engineering and the interval optimization technique.



The objectives and variables in the GICM are vectors of feasible intervals.



The GICM can identify noise sources and provide modification approaches.



A cascade tree of vehicle interior noise sources is constructed.