# Traffic Noise Prediction Applying Multivariate Bi-Directional Recurrent Neural Network

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

^{2}of 0.913. The proposed model was further compared to other classical empirical models such as the FHWA model. Several other works performed similar comparisons on different empirical or semi-dynamical traffic noise models against experiment data in [7,8,9,10]. The Burgess model, Griffith and Langdon, French CSTB model, Italian C.N.R model, French NMPB-Routes model and German RLS 90 model were explained with mathematic expressions. The authors of [11] discussed the road traffic noise in urban areas in the aspects of economy, society, law and regulation. The regional traffic noise models were briefly introduced, such as UK CoRTN model, US FHWA model, European Harmonoise/IMAGINE model and CNOSSOS model. The French NMPB 2008 is recommended as the reference model in forecasting urban traffic noise, by European Directive 2002/49/EC. In [12], the Nordic Prediction Method (NPM) and CNOSSOS models were compared to the measurement data, collected in 2013 at one hour interval within an entire day. The results showed that the CNOSSOS model has a smaller prediction root mean squared error (RMSE) than the NPM model. A typical empirical traffic noise prediction model usually has a very simple mathematical expression with a few parameters. In [13], a nested ensemble filtering (NEF) approach was performed for these parameters’ estimation and uncertainty quantification from the empirical model. The NEF approach was compared to the maximum likelihood estimation (MLE) method and outperformed the MLE approach in most conditions. The abovementioned French NMPB2008 and CNOSSOS-EU models are usually classified as semi-dynamic models, as they both consider proportion noise and rolling noise components separately in relation to traffic speed [14]. Although the CNOSSOS model is more advanced than most of the empirical models, it is not so easy to implement. A software implementation is needed, and practical guidelines for the input data design to test the real-world situation are limited [15]. A practical implementation of the CNOSSOS model was performed to predict urban noise in [16]. Heavy vehicle volume and velocity data were collected from an automatic monitoring station throughout the entire year of 2013. As a result, the values of sound pressure for heavy vehicles at each center frequency band was calculated with the CNOSSOS method.

## 2. Materials and Methods

#### 2.1. General Background of Recurrent Neural Network

#### 2.2. Architectures of RNN

#### 2.3. Model Evaluation Metrics

^{2}, is a proportion of explained variance of the model and the total variance of the data. The value of R

^{2}is usually between 0 and 1. An R

^{2}of 0 means a bad fit and 1 indicates a perfect fit, meaning that the model can explain 100% variance of the data. Mathematically, R

^{2}can be expressed as:

^{2}is a very common evaluation metric for regression tasks, it has some drawbacks, namely, the R

^{2}value always increases when the number of variables increases. Hence, adjusted R

^{2}has been introduced, which imposes a penalty for adding additional explanatory variables and only increases when a significant variable is added. The equation of adjusted R

^{2}is shown below:

^{2}and adjusted R

^{2}, mean squared error (MSE), root mean squared error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE) are also used in this work for model evaluation and comparison. MSE measures the average of the squares of errors. RMSE is the square root of MSE. MAE is a measure of the average of the absolute errors. MAPE measures the accuracy as an average percentage of the absolute errors divided by true values. The corresponding mathematical expressions could be found below:

#### 2.4. Experiment Setup and Data Acquisition

#### 2.5. Data Pre-Processing

#### 2.5.1. Video Data Pre-Processing

#### 2.5.2. Traffic Features Generation

#### 2.5.3. Audio Data Pre-Processing

#### 2.5.4. RNN Training Samples Generation

#### 2.5.5. Leave One Subject out Cross-Validation

#### 2.5.6. Data Scaling

## 3. Results and Discussion

#### 3.1. Development of RNN

#### 3.2. Results Comparison on Different Architectures

^{2}around 0.68, slightly better than the performance of Architecture 3 with an RMSE around 2.7 dB and an R

^{2}around 0.64, as shown in Figure 16a. However, as indicated in Figure 16b, the model training took a very long time with Architecture 1, almost 10 times longer computation time than Architecture 2; Architecture 1 trained 15 times more parameters than Architecture 2 by backpropagation, where the model based on Architecture 1 learned 590,430 parameters, and the model based on Architecture 2 learned 38,701 parameters. Architecture 3, in terms of both prediction accuracy and computation efficiency, does not have any privilege. Therefore, Architecture 2 was selected for training the recurrent neural network model.

#### 3.3. Results Comparison on Recurrent Units

^{2}, adjusted R

^{2}, RMSE, MAE and MAPE, are similar to each other. With the same configuration of the network, 48,201 parameters need to be trained in LSTM, while only 38,701 parameters need to be trained in GRU. As mentioned at the beginning, the GRU model is the simplified version of LSTM. It is also proven here that there is no additional cost of model performance, when using GRU instead of LSTM for Blansko traffic noise data modelling. Hence, the GRU model, with Architecture 2 (many-to-many), is the finalized traffic noise model for Blansko dataset.

#### 3.4. Model Hyperparameters Tuning

#### 3.5. Final Model Evaluation

#### 3.6. Comparison with CNOSSOS-EU Model

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Recurrent neural network (RNN) architecture: recurrent layer with a feedback loop, indicating the additional time dimension after unfolding it.

**Figure 3.**Illustration of long short-term memory (LSTM) unit, having three gates and a memory cell state.

**Figure 4.**Illustration of gated recurrent unit (GRU) unit, having two gates without dedicated memory cell state.

**Figure 5.**The appropriate RNN model architectures for traffic noise modelling, based on Blansko data: (

**a**) Many-to-one architecture: sequence input and single output. (

**b**) Many-to-many architecture: synced sequence input and sequence output. (

**c**) Encoder–decoder architecture: sequence input and sequence output (not necessary to be synced).

**Figure 6.**The camera scene over the roundabout, 3, 5, 6, 7, 8 refer to the locations of the microphones.

**Figure 7.**The audio recording setup: (

**a**) indication of microphone locations; (

**b**) picture of instruments used for audio recording.

**Figure 9.**Extracted SPL every other five minutes during the two days from different microphones: (

**a**) SPL every other five minutes from day 1; (

**b**) SPL every other five minutes from day 2.

**Figure 10.**An example illustration of generating training samples and validation samples for data augmentation (n_steps = 5).

**Figure 16.**GRU model performance comparison on different architectures: (

**a**) the accuracy comparison on different architectures; (

**b**) the computation cost comparison on different architectures.

**Figure 17.**GRU and LSTM performance comparison, described by prediction accuracy indicators (boxplots) and computation cost indicator (bar plot).

**Figure 18.**Model learning curve showing the reduction in training data error and validation data error over the GRU model training process.

**Figure 19.**Illustrations of captured and estimated SPL data over a selected time on each day (data from Mic 8): (

**a**) model prediction over a selected time on the first day; (

**b**) model prediction over a selected time on the second day.

**Figure 20.**Final model performance and residual distribution (data from Mic 8): (

**a**) comparison between predicted SPL values and actual SPL values based on testing data; (

**b**) the distribution of residuals based on testing data.

**Table 1.**Technical details of recording devices: (a) info of audio and video recorders: (b) info of microphones.

(a) | |||

Device Model | Sampling Rate | Number of Channels | |

Audio Recording | SQuadriga II | 48 KHz | 10 (6 × Line/ICP In, BHS In (2-channel), 2 × Pulse In) |

Video Recording | Hikvision IP camera | 30 fps | N.A. |

(b) | |||

Microphones | Frequency Response | Sensitivity (mV/Pa) | Max. Peak SPL (dB) |

Mic3 | 0.02–4 KHz (±0.5 dB) 4–20 KHz (±1.5 dB) | 51.3 | 130 |

Mic5 | 51.0 | ||

Mic6 | 51.6 | ||

Mic7 | 51.9 | ||

Mic8 | 52.0 |

Date | Start | End | Total Duration |
---|---|---|---|

Day 1 (30 September 2019) | 16:43 p.m. | 20:32 p.m. | 3 h 49 min |

Day 2 (1 October 2019) | 06:34 a.m. | 11:48 a.m. | 5 h 14 min |

Day 1 + Day 2 | - | - | 9 h 3 min |

Raw Data Frame | Vehicle Speed (km/h) | Vehicle Acceleration (m/s^{2}) | Vehicle Deceleration (m/s^{2}) | Vehicle Distance to Mic3 (m) | Vehicle Category | |
---|---|---|---|---|---|---|

Sample1 | Time step1 | [0.0058, 0.0034, 0.0033, 0.0043, 34.35, 31.57, 0.084, 31.61, 0.29, 8.01, 44.59, 0.0, 0.0, 27.83, 4.56, 31.02, 24.72, 31.22] | [0.0005, 0.0012, 0.0008, 0.004, 0.0, 0.0, 0.014, 0.81, 0.13, 1.89, 0.0, 0.0, 0.0, 8.42, 0.018, 3.29, 0.38, 0.0] | [0.0, 0.0, 0.0, 0.0, 3.26, 2.56, 0.0, 0.0, 0.0, 0.0, 2.12, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.26] | [39.08, 23.87, 22.70, 22.92, 68.57, 45.45, 55.99, 29.38, 46.05, 27.55, 53.53, 45.70, 22.82, 75.29, 47.44, 70.34, 94.37, 70.40] | [“car”, “car”, “car”, “car”, “car”, “car”, “car”, “car”, “car”, “heavy vehicle”, “car”, “car”, “car”, “car”, “car”, “car”, “car”, “small car”] |

… | … | … | … | … | … | … |

Sample800 | Time step800 | [33.61, 22.82, 17.68] | [1.44, 1.18, 1.19] | [0.0, 0.0, 0.0] | [41.69, 30.96, 30.01] | [“car”, “car”, “car”] |

… | … | … | … | … | … | … |

Features Representing Individual Vehicle (Raw Data) | Input Variables for Machine-Learning Model (after Preprocessing) |
---|---|

Vehicle category | [traffic volume, ratio of motorcycle, ratio of medium vehicle, ratio of heavy vehicle, ratio of bus, ratio of car, ratio of small car] |

Vehicle speed | [arithmetic mean, harmonic mean, min, max, median, range, mid-point, standard deviation, skewness, kurtosis] |

Vehicle acceleration | [arithmetic mean, min, max, median, range, mid-point, standard deviation, skewness, kurtosis] |

Vehicle deceleration | [arithmetic mean, min, max, median, range, mid-point, standard deviation, skewness, kurtosis] |

Vehicle distance to mics | [arithmetic mean, min, max, median, range, mid-point, standard deviation, skewness, kurtosis] |

Samples for Model Training | Model Evaluation | ||
---|---|---|---|

Training Data | Validation Data | Testing Data | |

Data Shape | (6276, 30, 44) | (2092, 30, 44) | (70, 30, 44) |

1st iteration | Mic3, 6, 7 | Mic5 | Mic8 |

2nd iteration | Mic3, 6, 8 | Mic5 | Mic7 |

3rd iteration | Mic3, 7, 8 | Mic5 | Mic6 |

4th iteration | Mic6, 7, 8 | Mic3 | Mic5 |

5th iteration | Mic6, 7, 8 | Mic5 | Mic3 |

Hyperparameter | Value |
---|---|

Number of layers | 3 (one bidirectional GRU layer, two dense layers) |

Number of neurons | 50, 100, 1 |

Learning rate | 0.0001 |

Batch size | 256 |

Optimization algorithm | Adam |

Dropout rate | 0.4 |

Sequence length (n_steps) | 30 |

Number of Epochs | 143 (controlled by Keras Early Stopping) |

R^{2} | Adjusted R^{2} | RMSE | MAE | MAPE | |
---|---|---|---|---|---|

1st iteration | 0.6953 | 0.6888 | 2.373 | 1.857 | 0.024 |

2nd iteration | 0.6629 | 0.6557 | 2.648 | 2.111 | 0.027 |

3rd iteration | 0.5359 | 0.526 | 2.993 | 2.406 | 0.030 |

4th iteration | 0.7766 | 0.7718 | 2.09 | 1.673 | 0.021 |

5th iteration | 0.7319 | 0.7262 | 2.136 | 1.848 | 0.024 |

Average | 0.6805 | 0.6737 | 2.448 | 1.979 | 0.0252 |

Standard dev. | 0.0816 | 0.0834 | 0.3371 | 0.2551 | 0.0031 |

Testing Data | RMSE | MAE | MAPE |
---|---|---|---|

Mic3 | 6.357 | 4.902 | 0.063 |

Mic5 | 7.706 | 6.294 | 0.079 |

Mic6 | 7.494 | 6.121 | 0.077 |

Mic7 | 7.189 | 5.659 | 0.072 |

Mic8 | 6.967 | 5.539 | 0.071 |

Average | 7.143 | 5.703 | 0.072 |

Standard dev. | 0.467 | 0.489 | 0.006 |

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**MDPI and ACS Style**

Zhang, X.; Kuehnelt, H.; De Roeck, W.
Traffic Noise Prediction Applying Multivariate Bi-Directional Recurrent Neural Network. *Appl. Sci.* **2021**, *11*, 2714.
https://doi.org/10.3390/app11062714

**AMA Style**

Zhang X, Kuehnelt H, De Roeck W.
Traffic Noise Prediction Applying Multivariate Bi-Directional Recurrent Neural Network. *Applied Sciences*. 2021; 11(6):2714.
https://doi.org/10.3390/app11062714

**Chicago/Turabian Style**

Zhang, Xue, Helmut Kuehnelt, and Wim De Roeck.
2021. "Traffic Noise Prediction Applying Multivariate Bi-Directional Recurrent Neural Network" *Applied Sciences* 11, no. 6: 2714.
https://doi.org/10.3390/app11062714