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This paper presents a back-propagation neural network model for sound quality prediction (BPNN-SQP) of multiple working conditions’ vehicle interior noise. According to the standards and regulations, four kinds of vehicle interior noises under operating conditions, including idle, constant speed, accelerating and braking, are acquired. The objective psychoacoustic parameters and subjective annoyance results are respectively used as the input and output of the BPNN-SQP model. With correlation analysis and significance test, some psychoacoustic parameters, such as loudness, A-weighted sound pressure level, roughness, articulation index and sharpness, are selected for modeling. The annoyance values of unknown noise samples estimated by the BPNN-SQP model are highly correlated with the subjective annoyances. Conclusion can be drawn that the proposed BPNN-SQP model has good generalization ability and can be applied in sound quality prediction of vehicle interior noise under multiple working conditions.

With the development of automobile industry, vehicle noise problem has been paid increasing attention all over the world. Correspondingly, sound quality has become an important index to measure the quality of automotive products. Recently, many studies related to sound quality evaluation (SQE) of vehicle noise have been investigated by researchers, and many achievements were acquired. Shu [

Vehicle interior noise signal under stationary working condition of a vehicle is easy to be measured and evaluated. The non-stationary interior noise, which keeps changing with the vehicle speed, is very complicated. How to evaluate the non-stationary sound so that the evaluated results can reflect perception of candidates accurately is a difficult problem for SQE engineers. It is important for modern vehicle to develop new methods, which can efficiently estimate the sound quality under multiple working conditions. Thus, based on the back- propagation neural network (BPNN), a SQP model for multi-working conditions’ vehicle interior noise is built in this paper. By this model, human auditory perception for vehicle interior noise can be described quantitatively with the model outputs, subjective annoyance values.

The BPNN [

Given the number of nodes of the input layer, the hidden and the output network n, k, m, respectively, the total number of input samples is

the k to the output layer of the j. For convenience, the threshold is included connection weights, and then the output of hidden layer node k is:

The output layer nodes for the node j:

where, standard sigmoid function is selected as incentive function:

The definition of global error functions can be expressed as:

where

a) The weight adjustment formula of output layer neurons:

where,

b) The weight adjustment formula of each hidden layer neurons:

The basic idea of the BP algorithm is the learning process and can be divided into two stages: the first stage (forward propagation process), given input information through a layer by layer processing each hidden layer and calculate the actual output value of each unit of

The vehicle noise signals under the conditions of idle, constant speed, accelerating and braking are acquired by road tests in this paper. The test conditions are carefully constructed referring to the measurement method for vehicle interior noise using GB/T 18697 standard [

Very terrible | Terrible | Very bad | Bad | Dissatisfied | Acceptable | Satisfied | Well | Good | Very good | Excellent |
---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |

Models/condition | A-weighted sound (dB) | Loudness (sone) | Sharpness (acum) | Roughness (asper) | Articulation index (%) | Annoyance |
---|---|---|---|---|---|---|

A/acceleration | 65.33 | 15.63 | 0.63 | 0.16 | 91.53 | 5.72 |

A/brake 60 | 61.21 | 12.85 | 0.77 | 0.13 | 95.24 | 4.33 |

A/brake 80 | 59.08 | 10.87 | 0.77 | 0.16 | 95.61 | 3.83 |

A/brake 100 | 61.21 | 13.17 | 0.75 | 0.18 | 93.5 | 3.06 |

A/constant 90 | 62.61 | 14.38 | 0.78 | 0.19 | 91.45 | 2.89 |

A/constant 90 | 61.21 | 13.43 | 0.79 | 0.23 | 93.37 | 2.11 |

A/constant 90 | 53.98 | 8.36 | 0.82 | 0.1 | 96.85 | 5.00 |

・・・ | ・・・ | ・・・ | ・・・ | ・・・ | ・・・ | ・・・ |

C/constant 100 | 62.27 | 15.07 | 0.97 | 0.79 | 86.36 | 5.13 |

C/acceleration | 63.81 | 17.72 | 1 | 0.23 | 70.96 | 5.56 |

C/brake 60 | 60.48 | 12.89 | 0.88 | 0.26 | 86.25 | 3.81 |

C/brake 80 | 58.58 | 13.11 | 1.28 | 0.46 | 91.95 | 4.48 |

For checking the correlations between calculated psychoacoustic indices and the subjective annoyance values, the SPSS software is adopted for Pearson correlation analysis. The correlation coefficients and two-tailed test results are listed in

According to the Pearson correlation analysis in

The BPNN-SQP model is constructed with MATLAB software in this paper. The measured 36 interior noise samples are used for model establishment. After relative analyzing and normalization processing, these data are divided into two groups, in which samples no. 1 - 24 are selected as training data, The rest samples no. 25 - 36 are used as testing data in order to verify the accuracy of the BPNN-SQP model. With correlation analysis and significance test, the final evaluation model is built within permissible error.

Sound annoyance has higher correlations with A-weighted sound pressure, loudness, AI index, and sharpness, as shown in

To build a uniform SQP model, signal amplitudes of the samples directly influence accuracy of the BPNN-SQP model. Before inputting the sample data to the model, sample normalizations should be conducted. In this paper, the sample data are compressed in a range of [0, 1], according to Equation (7).

The S-type of hidden layer and the linear output layer in a 3-layer BPNN can approximate any function [

Taking the optimal parameters obtained from the training data, the BPNN-SQP model with multi-working conditions is used to predict sound quality (annoyance) of vehicle interior noise. To check the model accuracy, firstly, the A-weighted SPLs, loudness, sharpness, AI index of the training samples are fed to as the model and the predicted annoyance values are compared with those from jury tests in

Taking the vehicle interior noises under multiple working conditions, this paper established a BPNN-SQP model, using some objective evaluation parameters, such as A-weighted sound level, loudness, AI index and sharpness

Parameters | SA | AW | L | AI | R | S | T | |
---|---|---|---|---|---|---|---|---|

SA | Pearson correlation | 1 | 0.661^{**} | 0.820^{**} | −0.770^{**} | −0.096 | 0.652^{*} | −0.173 |

Sig.(2-tailed) | 0.000 | 0.000 | 0.000 | 0.030 | 0.000 | 0.321 |

^{**}Correlation is significant at the 0.01 level (2-tailed); ^{*}Correlation is significant at the 0.05 level (2-tailed).

et al., as input, and subjective annoyance values as output. By applying this model to predict unknown noise samples, the averaged relative error of predicted results comparing with the actual results is 9.11%. The BPNN- SQP model for multi-condition of vehicle interior noise has high accuracy of prediction forecasting and good generalization ability.

This work has been supported by the NSFC (Grant no. 51175320), and partly supported by the Program for Special Appointment Professor (Eastern Scholar) at the Shanghai Institutions of Higher Learning, China.