Vehicle interior noise has emerged as a crucial assessment criterion for automotive NVH (Noise, Vibration, and Harshness). When analyzing the NVH performance of the vehicle body, the traditional SEA (Statistical Energy Analysis) simulation technology is usually limited by the accuracy of the material parameters obtained during the acoustic package modeling and the limitations of the application conditions. In order to effectively solve these shortcomings, based on the analysis of the vehicle noise transmission path, a multi-level objective decomposition architecture of the interior noise at the driver’s right ear is established. Combined with the data-driven method, the ResNet neural network model is introduced. The stacked residual blocks avoid the problem of gradient disappearance caused by the increasing network level of the traditional CNN network, thus establishing a higher-precision prediction model. This method alleviates the inherent limitations of traditional SEA simulation design, and enhances the prediction performance of the ResNet model by dynamically adjusting the learning rate. Finally, the proposed method is applied to a specific vehicle model and verified. The results show that the proposed method has significant advantages in prediction accuracy and robustness.

The acoustic package of a vehicle plays a critical role in determining the acoustic characteristics within the car. It not only reduces the noise level inside the vehicle but also allows for adjustments in sound quality to meet customer expectations of ride comfort. Consequently, conducting high-precision prediction research on the performance of the acoustic package is imperative for achieving the desired acoustic goals at the vehicle level. The front bulkhead package, floor package, and wheel arch package are major structural components responsible for shielding powertrain and tire noise sources, making them essential elements of the overall acoustic package. The effectiveness of their sound insulation directly impacts the overall Noise, Vibration, and Harshness (NVH) performance of the vehicle [

Previous studies have commonly employed the traditional acoustic finite element method to analyze in-car noise resulting from structural vibrations in automobiles [

Despite the challenges associated with accurately extracting parameter values for the material and characteristic parameters of the entire vehicle acoustic package through experimental processes, it is relatively easier to obtain underlying parameters of the acoustic package, such as the thickness of each material (e.g., sheet metal, sound insulation pads), the corresponding area proportions, coverage, and sound insulation performance of each material [

Moreover, the relationship between the underlying parameters of the acoustic package and its overall sound insulation performance exhibits a weak correlation. The transmission loss of components or paths associated with the acoustic package holds higher relevance. If an adaptive learning model is directly established without considering the sound insulation characteristics of the package components or paths, the complexity of the correlation between the underlying parameters and the top-level objectives significantly increases. This may lead to underfitting and adversely affect prediction accuracy [

For the prediction of vehicle interior noise performance, many nonlinear factors will be generated from the bottom design parameters of the acoustic package to the top-level design objectives. In the research, the disadvantages of the traditional SEA method should be eliminated and the complexity of data-driven mapping should be reduced. The present study introduces two contributions: (1) The utilization of data-driven techniques and hierarchical decomposition structure to analyze the accuracy of acoustic packages in predicting in-vehicle noise under diverse operating conditions. To achieve this, ResNet residual neural networks are employed, and the prediction accuracy is enhanced by implementing a dynamic learning rate. (2) Simultaneous prediction of in-vehicle noise performance at multiple frequencies under different operating conditions. To accomplish this, the paper proposes the DLR-ResNet approach for multi-objective prediction of in-vehicle noise across 17 one-third-octave intervals.

The structure of this paper is as follows: (1)

According to the noise transfer relationship of the acoustic package and the forward development process, the acoustic packages involved in the prediction of interior noise under different working conditions can be divided into system level and flat level. Based on this, the multi-level objective decomposition architecture of the interior noise acoustic package can be established as shown in

According to the decomposition architecture shown in

where,

According to the hierarchical decomposition architecture of

According to the multi-objective prediction model of interior noise above, it can be seen that interior noise is the prediction goal of this paper, that is, the optimization goal, and the design variable is the material composition, block thickness and block area of adjacent lower-level components connected to the main system-level acoustic package.

According to the decomposition architecture shown in

where,

In this paper, the residual network is proposed to solve the problem that the performance of neural networks decreases with the increase of network depth [

where,

The pooling layer downsamples the input feature map to reduce the data feature dimension [

where,

where,

In addition, to forward propagation, convolutional neural networks also have back propagation characteristics. The backpropagation process updates the model parameters based on the error calculated by the loss function [

where,

where,

Practically, as the number of layers deepens during the training process of the CNN network, the problem of network gradient disappearance occurs. Huang et al. [

Compared with the CNN network structure, ResNet uses Shortcut connections [

The typical structure of ResNet is shown in

Although ResNet deep neural networks have many of the above advantages over CNN networks, ResNet, like any model, has certain weaknesses, such as requiring a large amount of data for training and reasoning, over-reliance on data, and in some cases, ResNet may overfit, resulting in poor generalization. Therefore, this paper weakens the problem of directly using ResNet by combining the ResNet neural network with the multi-level objective decomposition architecture of the acoustic package described in

The test data for this study was obtained from a real vehicle test conducted on a class A car. To minimize the impact of varying noise environments on the interior noise test data, two specific working conditions were selected: medium speed and high speed of the hub belt vehicle. The interior noise, specifically above 200 Hz, was considered as representative of the overall interior noise. In accordance with the International Society of Automotive Engineers standard SAE J1400 [

In addition, to collect enough data to establish the mapping model between the acoustic package parameters and the interior noise of the vehicle with different frequencies, different acoustic package schemes are introduced in the test. According to the sound insulation characteristics, the main acoustic package of the test vehicle can be divided into five major systems: front panel, front floor, rear floor, front hub pack, and rear hub pack, as shown in

To further analyze the relationship between the performance of the acoustic package and the sound quality of the interior noise, the STL characteristics of the acoustic package system and components were measured by the reverberation chamber-anechoic chamber combination [

Equipment | Type | Instrumentation manufacturer | |
---|---|---|---|

1 | 16-channel data acquisition front-end | SIMENS-SCM2 | SIMENS |

2 | Sound pressure transducer | BSWA-MPA201 | BSWA |

3 | Acoustic pressure sensor calibrator | BSWA-CA114 | BSWA |

4 | Volume sound source | Bruel-M4292 | Bruel |

5 | Sound intensity probe | Bruel-3654 | Bruel |

6 | Microphone | GRAS-32HF | GRAS |

7 | Computer | HP-AMD Ryzen5 | Hewlett-Packard |

8 | Data acquisition software | Simcenter.Testlab18 | SIMENS |

In addition to the acoustic characteristics of acoustic package systems and components, acoustic materials consisting of acoustic package components are also crucial. Due to the large number of acoustic materials and their many general parameters, automotive companies generally build acoustic database systems for parameter invocation.

As shown in

Before building the prediction model of the sound insulation performance of the vehicle body system, it is necessary to prepare relevant data and preprocess the data. The collection of samples is mainly obtained through relevant sound insulation performance tests. The tire noise source data is obtained through bench tests. The collected samples are cleaned to reduce data noise. After completing the data pre-processing, because the data dimension and value will have a certain impact on the modeling, it is necessary to further normalize the data set [

where,

The software used for this article is Python 3.9, the deep learning library used is Pytorch 1.10.2, and the AMD Ryzen 5 4500U with Radeon Graphics and 16 G memory is configured.

Through the experimental test, the accurate interior noise data under different working conditions, the transmission loss of the main system acoustic package system, and the underlying parameters obtained from the database are obtained. Based on the improvement of the data samples, the ResNet method using the dynamic learning rate is introduced and combined with the multi-level objective decomposition architecture to establish an effective acoustic package forward development model suitable for engineering applications. For the sound insulation performance objective, when constructing the third-level to the second-level model, a plate-level basic data prediction system-level transmission loss prediction model is established. The thickness area ratio of sheet metal and sound package sound insulation pad materials and the sound insulation corresponding to 17 one-third frequency doubling points of each thickness are used as inputs, and the main system-level transmission loss corresponding to each plate level is used as output. When constructing the second-level to the first-level model, the main system sound package and tire noise source are used as the input of the model, and the interior noise (the interior noise in the driver’s right ear) is used as the output of the model. In the test results, 400 groups of samples were randomly selected as the training set, the remaining 100 groups were used as the test set for learning, and the root mean square error (RMSE) index is used to test the accuracy of the model, the root mean square error formula is visible (8), the closer the RMSE index is to 0, the higher the accuracy of the model, the smaller the error of the predicted value, and the generalization of the model is strong. For the adjacent levels in the multi-level objective decomposition architecture, the two-layer DLR-ResNet network is selected as the sub-model for modeling. The number of input layer nodes of each sub-model is the input data dimension, and the output layer is the result after a full connection.

After network learning, the prediction results and model accuracy at 17 one-third frequencies can be obtained. As shown in _{1}^{[1]} and _{1}^{[2]} in the training set and test set are shown, respectively. Among them, the maximum relative error of the above model is 4.52% of _{1}^{[1]} and 4.74% of _{1}^{[1]} in the training set and the test set, respectively. _{1}^{[1]} is less than 0.03. At the same time, the RMSE of the second-level model is not higher than 0.04. Secondly, the comparison results of

Data set | Objective | First–Second level (RMSE) | Second–Third level (RMSE) |
---|---|---|---|

Rmse (_{1}^{[2]}) = 0.032 |
|||

Rmse (_{2}^{[2]}) = 0.029 |
|||

Training set | RMSE | Rmse (_{1}^{[1]}) = 0.026 |
Rmse (_{3}^{[2]}) = 0.030 |

Rmse (_{4}^{[2]}) = 0.028 |
|||

Rmse (_{5}^{[2]}) = 0.031 |
|||

Rmse (_{1}^{[2]}) = 0.038 |
|||

Rmse (_{2}^{[2]}) = 0.032 |
|||

Testing set | RMSE | Rmse (_{1}^{[1]}) = 0.028 |
Rmse (_{3}^{[2]}) = 0.033 |

Rmse (_{4}^{[2]}) = 0.031 |
|||

Rmse (_{5}^{[2]}) = 0.034 |

In the previous chapter, the multi-objective prediction of vehicle interior noise has been analyzed, especially the model accuracy at 1250 Hz is explained. Therefore, both local accuracy and overall accuracy show that DLR-ResNet residual network has more prominent advantages in the performance prediction of vehicle interior noise, and has better robustness and generalization. Therefore, based on the multi-level objective decomposition architecture of vehicle interior noise and the DLR-ResNet model, the multi-objective optimization of the sound pressure level of vehicle interior noise at 17 one-third octaves is carried out, in which weight and cost are taken as constraints. Finally, an example is given according to the optimization results of vehicle interior noise peak at 1250 Hz proposed in

Combined with the economic principle of actual acoustic package development, the weighted constraint is introduced to set different weight coefficients for cost and weight. In this study, to make the optimization results more universal, the weight coefficients of cost and weight are designed to be 0.5 and 0.5. The design variables are all five main systems: the front wall system, the front floor system, the rear floor system, the left rear hub package system, and the right rear hub package system. The block thickness and the area ratio of different thicknesses of each component of the front wall system, the front floor system, the rear floor system, the left rear hub package system, and the right rear hub package system. According to the engineering feasibility, the design space is in the range of ±20% of the variables based on the original value. There are two constraints: 1) The maximum thickness of the acoustic package of each main system is not greater than its maximum thickness in the original state, and 2) The sum of the area ratios corresponding to different thicknesses of each component is 100%. The established optimization model is shown in

where,

The Latin hypercube algorithm has the advantages of good scalability and non-degeneration [

Part name | Material name | Original thickness (mm) | Original area ratio (%) | Optimized thickness (mm) | Optimized area ratio (%) |
---|---|---|---|---|---|

Front wall metal | 45 Steel | 0.8 | 30.0 | 0.9 | 28.0 |

1.0 | 70.0 | 1.2 | 72.0 | ||

Out-front wall pad | Fiber glass | 15.0 | 28.0 | 16.0 | 26.0 |

25.0 | 72.0 | 27.0 | 74.0 | ||

In-front wall pad | PU foam | 6.0 | 36.0 | 5.5 | 34.0 |

11.0 | 64.0 | 10.0 | 66.0 | ||

Cotton felt | 4.0 | 27.0 | 6.0 | 26.0 | |

6.0 | 73.0 | 8.0 | 74.0 | ||

Front floor metal | 45 Steel | 0.7 | 29.0 | 0.9 | 35.0 |

1.2 | 61.0 | 1.3 | 65.0 | ||

Front floor carpet | PU foam | 5.0 | 33.0 | 7.0 | 30.0 |

12.0 | 67.0 | 11.0 | 70.0 | ||

Cotton felt | 3.0 | 28.0 | 4.0 | 24.0 | |

5.0 | 72.0 | 5.0 | 76.0 |

State | SPL (dB) | Cost (yuan) | Weight (kg) | Constraint weighted value | |
---|---|---|---|---|---|

Original state | 59.6 | 502 | 251 | 1.045 | |

Optimized result | Predicted value | 57.2 | 486 | 237 | 0.92 |

Measured value | 57.4 | 489 | 240 | 0.95 |

Note: The above results are optimization results at 1250 Hz frequency, as well as other frequency analyses, and the optimization results are reduced compared with the original data.

According to

In order to reduce the problem of overfitting or over-reliance on data reasoning caused by neural networks, this section builds a multi-level objective decomposition architecture, and with the support of this mechanism, ResNet neural networks are introduced to make multi-objective prediction of top-level in-vehicle noise at different frequencies, and compare with CNN networks and the prediction results of DLR-ResNet networks proposed in this paper. The results show that the DLR-ResNet network proposed in this paper has the advantages of higher accuracy and generalization for multi-objective prediction of acoustic packets, and the DLR-ResNet network model is selected as the optimization tool for acoustic packets, and the Latin hypercube experimental design is used as a means of multi-objective optimization, and the optimization results are close to the measured results, which verifies the accuracy and effectiveness of the proposed method.

This paper presents the DLR-ResNet approach, which aims to analyze the in-cabin noise performance in automobiles across 17 one-third octave bands. By considering the noise transmission relationship and hierarchical objective decomposition, a multi-level objective prediction and optimization method for the acoustic package is proposed and validated using an actual vehicle model. The DLR-ResNet method achieves a prediction accuracy of over 98% for the interior noise performance at each frequency, surpassing both the basic CNN model and the simple ResNet model. Furthermore, the study constructs a multi-level architecture model for vehicle interior noise, reducing the nonlinearity and complexity of the overall prediction model. This approach also mitigates the limitations associated with model training caused by excessive design parameters and parameter redundancy. The optimization results based on this model closely align with the measured results, with a relative error of only 0.8% for the two performance objectives. The optimized measured results indicate improvements of 3.6%, 2.6%, and 4.4% in vehicle interior noise performance, cost, and weight, respectively, compared to the original values. These findings confirm the effectiveness and accuracy of the proposed method.

The prediction and optimization methods proposed in this paper for the multi-objective acoustic package performance research can provide some reference for subsequent scholars. However, this paper only studies the sound insulation performance and interior noise of the body system for a certain A-class model, and it is necessary to further explore and test more models in the next research to improve the migration ability and generalization ability of the model. However, the optimization of acoustic package only adopts the method of experimental design, which has certain limitations, and there may be situations where the optimization result is not optimal, so in the next step of research, multi-objective intelligent optimization algorithm can be used to explore, such as multi-objective particle swarm optimization algorithm, multi-objective genetic algorithm, NSGA-II algorithm, etc., and better combine the intelligent optimization algorithm with the machine learning prediction model.

The adjacent upper-level design objective

The proposed calculation level in the hierarchical decomposition architecture

The total number of layers of the hierarchical decomposition architecture

The number of design goals of the level

The prediction model

The design variable of the adjacent lower level

The number of design variables of the level

The optimization objective

The number of design variables of the level

The number of design variables of the level

The optimization objective of the adjacent upper level

An inequality constraint condition

The equality constraint condition

The design variable

The upper limits of the design variable

The i-th channel of the l-layer feature map

The j-th kernel, and

The convolutional layer

The feature map of the j-th channel of the

The output feature after the pooling operation of the 0th feature map

The element

The weight of connecting neurons

The loss of the t-th iteration is expressed

The number of samples

The true value of the i-th sample

The data to be normalized

A vector of rows consisting of the smallest values in each column

The row vector consisting of the maximum value in each column

The maximum value of the interval to be mapped to, which defaults to 1

The minimum value of the interval to map to, which defaults to 0

The result of normalization

The optimization constraint cost

The weight

The normalization constants of the optimization constraint cost

The thickness parameter

The area ratio parameter

The authors would like to acknowledge the support from the Sichuan Provincial Natural Science Foundation and the facilities provided by the Institute of Energy and Power Research at Southwest Jiaotong University for the experimental research.

This research was funded by the SWJTU Science and Technology Innovation Project, Grant Number 2682022CX008; and the Natural Science Foundation of Sichuan Province, Grant Numbers 2022NSFSC1892, 2023NSFSC0395.

The authors confirm contribution to the paper as follows: conceptualization, writing-original draft: Yunru Wu; resources, supervision, funding acquisition: Haibo Huang, Mingliang Yang; methodology: Xiangbo Liu; writing-review and editing: Weiping Ding. All authors reviewed the results and approved the final version of the manuscript.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest to report regarding the present study.