#### Source: Applus IDIADA

**ADELANTO, Calif. – The following is the first of three Technical Corner pieces by Antonio Rubio, Project Manager, Braking Systems at Applus IDIADA, on how the use of artificial intelligence can help in the development of braking systems NVH characteristics.**

Braking systems development is currently facing some huge challenges. The first one is electrification. The presence of regenerative braking and the standard adoption of electro-hydraulic braking systems is completely changing the way braking systems are developed and validated.

The second one is connectivity. This concept is not only applying to the vehicle itself, but also to the development process. Currently vehicles are tested in multiple locations on a worldwide basis. Witnessing testing is becoming every day more expensive and complicated, particularly for vehicles which are sold in different markets.

The third big challenge is certainly the increasing level of driving automation. The pure concept of vehicle assessment and sign-off is shifted from the driver perspective to the “occupant” perspective. Comfort cannot be jeopardized, a good balance between performance and refinement must be guaranteed.

In order to respond to these three big challenges to brake development, the authors are presenting how artificial intelligence can support the identification of brake noise in real time. In this paper a summary of the machine learning techniques used to identify brake noise events are presented.

Particularly, the validation of the algorithm is presented in order to cover not only brake squeal in standard condition, but also to detect different brake noises, under different testing conditions (different standards, city and mountain driving, low and high ambient temperature, different vehicle category).

Finally, the authors are presenting an automatic process which is managing the complete process, from driving and rating, through detection, brake noise automated analysis and finally the upload of the testing report and relevant information in a connected secure environment.

1.**Introduction**

Three main sections will be presented to the reader. First, the mathematical background of the study will be summarized, then a specific explanation of the machine learning techniques used in order to define and train the detection algorithm will be provided. In the third section, some validation data will also be provided, with some special focus on the analysis of reliability on a wide range of scenarios. In the last paragraphs, the authors are explaining the industrial application of this technology into open road vehicle testing.

2.**Mathematical Background**

2.1 Spectrogram calculation

This work consists in detecting squeal in an automated way by using a machine learning algorithm. The recognition of the squeal is based on three steps:

- To import the microphone data for each wheel
- To compute the spectrogram
- To develop the machine learning algorithm
- Firstly, we import the sound from the microphone for each wheel and pressure expressed in Pascal. The final goal is to represent the frequencies of the sound as an image. To obtain this, a mathematical tool, known as spectrogra and used in audio spectral analysis is exploited.
- The spectrogram is a visual way (usually on a logarithmic scale, such as decibel) of representing the Short-Time Fourier Transformation (STFT) magnitude. The STFT is a sequence of Fast Fourier Transforms (FFTs) of windowed data segments, where the windows are usually allowed to overlap in time.
- In this study, the spectrogram is computed by using the Hanning window with an overlap in time, typically between 50%-80%. The Hanning window is defined as

where *M* is the number of points in the output window. It is established that the value *M* is equal to length of the Fast Fourier Transform. To compute the spectrogram, the sampling frequency *f _{s}* equal to 40000 Hz is used. In general, the sampling frequency is a variable value, but it needs to satisfy the conditions of Nyquist-Shannon theorem, in fact

*f*must be at least the double of 20000 Hz.

_{s}The spectrogram is a two-dimensional graph, with a third dimension represented by a colormap. In particular, the horizontal axis represents the time and the vertical axis represents the frequency, with the lowest frequencies at the bottom and the highest frequencies at the top. The third dimension indicates the amplitude of a frequency at a particular time and it is represented by the intensity of color of each point in the image.

The spectrogram can be represented as an array with m rows and n columns, where m is the dimension of the array of sample frequencies and n is the dimension of the array of the segment times. The sampling is done in according with the Nyquist-Shannon sampling theorem.

In this work, the spectrogram is expressed in acoustic decibel. The methodology to obtain this is expressed as follows.

Figure 1 Spectrogram example in acoustic decibels

It is considered an array *F* of frequencies of dimension *mx1*, defined such that

Where *f _{s}* is the sampling frequency. Now a filter for each entry of the frequency vector

*F*is applied.

Therefore, the filter *W _{A}(f)*, that is a function of

*F*and it is defined in the following way, is considered:

for each *i*=1,…,m and *f _{i}* indicates the entry of frequency vector

*F*. An array of dimension

*mx1*is considered.

The last step is to compute the linear decibel and to join it with the filter *W _{A}(f_{i})*. Therefore, after computing the Short Time Fourier Transformation magnitude of the sound, an array

*T*with

*m*rows and

*n*columns is obtained. To obtain the linear decibel the following formula (𝑑𝐵

_{𝐿}) is computed for each entry of

*T*the following formula,

where *t _{ij}* indicates the entry of the array

*T*and

*ref*is the reference frequency; a 𝑟𝑒𝑓=20∗10

^{−6}Hz frequency is considered. Therefore, the acoustic decibel 𝑑𝐵

_{𝐴}is computed in the following way

where 𝑑𝐵_{𝐴}, 𝑑𝐵_{𝐿} and 𝑊_{𝐴} are arrays with m rows and n columns, in particular 𝑊_{𝐴} contains for each column the same element of 𝑊_{𝐴}(𝑓). In other word 𝑊_{𝐴} is a replica of the array 𝑊_{𝐴}(𝑓) for *n* columns.

#### About Applus IDIADA

With more than 25 years’ experience and 2,450 engineers specializing in vehicle development, Applus IDIADA is a leading engineering company providing design, testing, engineering, and homologation services to the automotive industry worldwide.

Applus IDIADA has locations in California and Michigan, with further presence in 25 other countries, mainly in Europe and Asia.

Tags: NVH, Braking, Applus+IDIADA